diff --git a/docs/source/reference-core.rst b/docs/source/reference-core.rst
index 333cb0537b..a6dc5b1f5a 100644
--- a/docs/source/reference-core.rst
+++ b/docs/source/reference-core.rst
@@ -1827,8 +1827,8 @@ to spawn a child thread, and then use a :ref:`memory channel
 
    The ``from_thread.run*`` functions reuse the host task that called
    :func:`trio.to_thread.run_sync` to run your provided function, as long as you're
-   using the default ``cancellable=False`` so Trio can be sure that the task will remain
-   around to perform the work. If you pass ``cancellable=True`` at the outset, or if
+   using the default ``abandon_on_cancel=False`` so Trio can be sure that the task will remain
+   around to perform the work. If you pass ``abandon_on_cancel=True`` at the outset, or if
    you provide a :class:`~trio.lowlevel.TrioToken` when calling back in to Trio, your
    functions will be executed in a new system task. Therefore, the
    :func:`~trio.lowlevel.current_task`, :func:`current_effective_deadline`, or other
@@ -1836,7 +1836,7 @@ to spawn a child thread, and then use a :ref:`memory channel
 
 You can also use :func:`trio.from_thread.check_cancelled` to check for cancellation from
 a thread that was spawned by :func:`trio.to_thread.run_sync`. If the call to
-:func:`~trio.to_thread.run_sync` was cancelled (even if ``cancellable=False``!), then
+:func:`~trio.to_thread.run_sync` was cancelled, then
 :func:`~trio.from_thread.check_cancelled` will raise :func:`trio.Cancelled`.
 It's like ``trio.from_thread.run(trio.sleep, 0)``, but much faster.
 
diff --git a/newsfragments/2841.deprecated.rst b/newsfragments/2841.deprecated.rst
new file mode 100644
index 0000000000..687573f39a
--- /dev/null
+++ b/newsfragments/2841.deprecated.rst
@@ -0,0 +1,8 @@
+To better reflect the underlying thread handling semantics,
+the keyword argument for `trio.to_thread.run_sync` that was
+previously called ``cancellable`` is now named ``abandon_on_cancel``.
+It still does the same thing -- allow the thread to be abandoned
+if the call to `trio.to_thread.run_sync` is cancelled -- but since we now
+have other ways to propagate a cancellation without abandoning
+the thread, "cancellable" has become somewhat of a misnomer.
+The old ``cancellable`` name is now deprecated.
diff --git a/trio/_socket.py b/trio/_socket.py
index efef2ff5ed..061cc09367 100644
--- a/trio/_socket.py
+++ b/trio/_socket.py
@@ -240,7 +240,7 @@ def numeric_only_failure(exc: BaseException) -> bool:
             type,
             proto,
             flags,
-            cancellable=True,
+            abandon_on_cancel=True,
         )
 
 
@@ -261,7 +261,7 @@ async def getnameinfo(
         return await hr.getnameinfo(sockaddr, flags)
     else:
         return await trio.to_thread.run_sync(
-            _stdlib_socket.getnameinfo, sockaddr, flags, cancellable=True
+            _stdlib_socket.getnameinfo, sockaddr, flags, abandon_on_cancel=True
         )
 
 
@@ -272,7 +272,7 @@ async def getprotobyname(name: str) -> int:
 
     """
     return await trio.to_thread.run_sync(
-        _stdlib_socket.getprotobyname, name, cancellable=True
+        _stdlib_socket.getprotobyname, name, abandon_on_cancel=True
     )
 
 
diff --git a/trio/_subprocess_platform/waitid.py b/trio/_subprocess_platform/waitid.py
index 756741218f..44c8261074 100644
--- a/trio/_subprocess_platform/waitid.py
+++ b/trio/_subprocess_platform/waitid.py
@@ -72,14 +72,14 @@ async def _waitid_system_task(pid: int, event: Event) -> None:
     """Spawn a thread that waits for ``pid`` to exit, then wake any tasks
     that were waiting on it.
     """
-    # cancellable=True: if this task is cancelled, then we abandon the
+    # abandon_on_cancel=True: if this task is cancelled, then we abandon the
     # thread to keep running waitpid in the background. Since this is
     # always run as a system task, this will only happen if the whole
     # call to trio.run is shutting down.
 
     try:
         await to_thread_run_sync(
-            sync_wait_reapable, pid, cancellable=True, limiter=waitid_limiter
+            sync_wait_reapable, pid, abandon_on_cancel=True, limiter=waitid_limiter
         )
     except OSError:
         # If waitid fails, waitpid will fail too, so it still makes
diff --git a/trio/_tests/test_threads.py b/trio/_tests/test_threads.py
index 86d59b4dbb..4002a0e808 100644
--- a/trio/_tests/test_threads.py
+++ b/trio/_tests/test_threads.py
@@ -29,6 +29,7 @@
     CancelScope,
     CapacityLimiter,
     Event,
+    TrioDeprecationWarning,
     _core,
     fail_after,
     move_on_after,
@@ -337,10 +338,10 @@ def f(q: stdlib_queue.Queue[str]) -> None:
         q.get()
         register[0] = "finished"
 
-    async def child(q: stdlib_queue.Queue[None], cancellable: bool) -> None:
+    async def child(q: stdlib_queue.Queue[None], abandon_on_cancel: bool) -> None:
         record.append("start")
         try:
-            return await to_thread_run_sync(f, q, cancellable=cancellable)
+            return await to_thread_run_sync(f, q, abandon_on_cancel=abandon_on_cancel)
         finally:
             record.append("exit")
 
@@ -402,7 +403,7 @@ def thread_fn() -> None:
 
     async def main() -> None:
         async def child() -> None:
-            await to_thread_run_sync(thread_fn, cancellable=True)
+            await to_thread_run_sync(thread_fn, abandon_on_cancel=True)
 
         async with _core.open_nursery() as nursery:
             nursery.start_soon(child)
@@ -491,7 +492,10 @@ def thread_fn(cancel_scope: CancelScope) -> None:
         async def run_thread(event: Event) -> None:
             with _core.CancelScope() as cancel_scope:
                 await to_thread_run_sync(
-                    thread_fn, cancel_scope, limiter=limiter_arg, cancellable=cancel
+                    thread_fn,
+                    cancel_scope,
+                    abandon_on_cancel=cancel,
+                    limiter=limiter_arg,
                 )
             print("run_thread finished, cancelled:", cancel_scope.cancelled_caught)
             event.set()
@@ -553,7 +557,7 @@ def release_on_behalf_of(self, borrower: Task) -> None:
 
     # TODO: should CapacityLimiter have an abc or protocol so users can modify it?
     # because currently it's `final` so writing code like this is not allowed.
-    await to_thread_run_sync(lambda: None, limiter=CustomLimiter())  # type: ignore[arg-type]
+    await to_thread_run_sync(lambda: None, limiter=CustomLimiter())  # type: ignore[call-overload]
     assert record == ["acquire", "release"]
 
 
@@ -571,7 +575,7 @@ def release_on_behalf_of(self, borrower: Task) -> NoReturn:
     bs = BadCapacityLimiter()
 
     with pytest.raises(ValueError) as excinfo:
-        await to_thread_run_sync(lambda: None, limiter=bs)  # type: ignore[arg-type]
+        await to_thread_run_sync(lambda: None, limiter=bs)  # type: ignore[call-overload]
     assert excinfo.value.__context__ is None
     assert record == ["acquire", "release"]
     record = []
@@ -580,7 +584,7 @@ def release_on_behalf_of(self, borrower: Task) -> NoReturn:
     # chains with it
     d: dict[str, object] = {}
     with pytest.raises(ValueError) as excinfo:
-        await to_thread_run_sync(lambda: d["x"], limiter=bs)  # type: ignore[arg-type]
+        await to_thread_run_sync(lambda: d["x"], limiter=bs)  # type: ignore[call-overload]
     assert isinstance(excinfo.value.__context__, KeyError)
     assert record == ["acquire", "release"]
 
@@ -881,7 +885,7 @@ async def test_trio_token_weak_referenceable() -> None:
     assert token is weak_reference()
 
 
-async def test_unsafe_cancellable_kwarg() -> None:
+async def test_unsafe_abandon_on_cancel_kwarg() -> None:
     # This is a stand in for a numpy ndarray or other objects
     # that (maybe surprisingly) lack a notion of truthiness
     class BadBool:
@@ -889,7 +893,7 @@ def __bool__(self) -> bool:
             raise NotImplementedError
 
     with pytest.raises(NotImplementedError):
-        await to_thread_run_sync(int, cancellable=BadBool())  # type: ignore[arg-type]
+        await to_thread_run_sync(int, abandon_on_cancel=BadBool())  # type: ignore[call-overload]
 
 
 async def test_from_thread_reuses_task() -> None:
@@ -933,7 +937,7 @@ def sync_check() -> None:
     assert not queue.get_nowait()
 
     with _core.CancelScope() as cancel_scope:
-        await to_thread_run_sync(sync_check, cancellable=True)
+        await to_thread_run_sync(sync_check, abandon_on_cancel=True)
 
     assert cancel_scope.cancelled_caught
     assert not await to_thread_run_sync(partial(queue.get, timeout=1))
@@ -957,7 +961,7 @@ def async_check() -> None:
     assert not queue.get_nowait()
 
     with _core.CancelScope() as cancel_scope:
-        await to_thread_run_sync(async_check, cancellable=True)
+        await to_thread_run_sync(async_check, abandon_on_cancel=True)
 
     assert cancel_scope.cancelled_caught
     assert not await to_thread_run_sync(partial(queue.get, timeout=1))
@@ -976,11 +980,11 @@ async def async_time_bomb() -> None:
 async def test_from_thread_check_cancelled() -> None:
     q: stdlib_queue.Queue[str] = stdlib_queue.Queue()
 
-    async def child(cancellable: bool, scope: CancelScope) -> None:
+    async def child(abandon_on_cancel: bool, scope: CancelScope) -> None:
         with scope:
             record.append("start")
             try:
-                return await to_thread_run_sync(f, cancellable=cancellable)
+                return await to_thread_run_sync(f, abandon_on_cancel=abandon_on_cancel)
             except _core.Cancelled:
                 record.append("cancel")
                 raise
@@ -1009,7 +1013,7 @@ def f() -> None:
     # implicit assertion, Cancelled not raised via nursery
     assert record[1] == "exit"
 
-    # cancellable=False case: a cancel will pop out but be handled by
+    # abandon_on_cancel=False case: a cancel will pop out but be handled by
     # the appropriate cancel scope
     record = []
     ev = threading.Event()
@@ -1025,7 +1029,7 @@ def f() -> None:
     assert "cancel" in record
     assert record[-1] == "exit"
 
-    # cancellable=True case: slightly different thread behavior needed
+    # abandon_on_cancel=True case: slightly different thread behavior needed
     # check thread is cancelled "soon" after abandonment
     def f() -> None:  # type: ignore[no-redef] # noqa: F811
         ev.wait()
@@ -1068,9 +1072,25 @@ async def test_reentry_doesnt_deadlock() -> None:
 
     async def child() -> None:
         while True:
-            await to_thread_run_sync(from_thread_run, sleep, 0, cancellable=False)
+            await to_thread_run_sync(from_thread_run, sleep, 0, abandon_on_cancel=False)
 
     with move_on_after(2):
         async with _core.open_nursery() as nursery:
             for _ in range(4):
                 nursery.start_soon(child)
+
+
+async def test_cancellable_and_abandon_raises() -> None:
+    with pytest.raises(ValueError):
+        await to_thread_run_sync(bool, cancellable=True, abandon_on_cancel=False)  # type: ignore[call-overload]
+
+    with pytest.raises(ValueError):
+        await to_thread_run_sync(bool, cancellable=True, abandon_on_cancel=True)  # type: ignore[call-overload]
+
+
+async def test_cancellable_warns() -> None:
+    with pytest.warns(TrioDeprecationWarning):
+        await to_thread_run_sync(bool, cancellable=False)
+
+    with pytest.warns(TrioDeprecationWarning):
+        await to_thread_run_sync(bool, cancellable=True)
diff --git a/trio/_threads.py b/trio/_threads.py
index fc0346f283..a1859a928a 100644
--- a/trio/_threads.py
+++ b/trio/_threads.py
@@ -8,14 +8,13 @@
 import threading
 from collections.abc import Awaitable, Callable
 from itertools import count
-from typing import Generic, TypeVar
+from typing import Generic, TypeVar, overload
 
 import attr
 import outcome
 from sniffio import current_async_library_cvar
 
 import trio
-from trio._core._traps import RaiseCancelT
 
 from ._core import (
     RunVar,
@@ -24,6 +23,8 @@
     enable_ki_protection,
     start_thread_soon,
 )
+from ._core._traps import RaiseCancelT
+from ._deprecate import warn_deprecated
 from ._sync import CapacityLimiter
 from ._util import coroutine_or_error
 
@@ -171,13 +172,36 @@ def run_in_system_nursery(self, token: TrioToken) -> None:
         token.run_sync_soon(self.run_sync)
 
 
-@enable_ki_protection  # Decorator used on function with Coroutine[Any, Any, RetT]
+@overload  # Decorator used on function with Coroutine[Any, Any, RetT]
+async def to_thread_run_sync(  # type: ignore[misc]
+    sync_fn: Callable[..., RetT],
+    *args: object,
+    thread_name: str | None = None,
+    abandon_on_cancel: bool = False,
+    limiter: CapacityLimiter | None = None,
+) -> RetT:
+    ...
+
+
+@overload  # Decorator used on function with Coroutine[Any, Any, RetT]
 async def to_thread_run_sync(  # type: ignore[misc]
     sync_fn: Callable[..., RetT],
     *args: object,
     thread_name: str | None = None,
     cancellable: bool = False,
     limiter: CapacityLimiter | None = None,
+) -> RetT:
+    ...
+
+
+@enable_ki_protection  # Decorator used on function with Coroutine[Any, Any, RetT]
+async def to_thread_run_sync(  # type: ignore[misc]
+    sync_fn: Callable[..., RetT],
+    *args: object,
+    thread_name: str | None = None,
+    abandon_on_cancel: bool | None = None,
+    cancellable: bool | None = None,
+    limiter: CapacityLimiter | None = None,
 ) -> RetT:
     """Convert a blocking operation into an async operation using a thread.
 
@@ -198,8 +222,8 @@ async def to_thread_run_sync(  # type: ignore[misc]
       sync_fn: An arbitrary synchronous callable.
       *args: Positional arguments to pass to sync_fn. If you need keyword
           arguments, use :func:`functools.partial`.
-      cancellable (bool): Whether to allow cancellation of this operation. See
-          discussion below.
+      abandon_on_cancel (bool): Whether to abandon this thread upon
+          cancellation of this operation. See discussion below.
       thread_name (str): Optional string to set the name of the thread.
           Will always set `threading.Thread.name`, but only set the os name
           if pthread.h is available (i.e. most POSIX installations).
@@ -225,17 +249,17 @@ async def to_thread_run_sync(  # type: ignore[misc]
     starting the thread. But once the thread is running, there are two ways it
     can handle being cancelled:
 
-    * If ``cancellable=False``, the function ignores the cancellation and
+    * If ``abandon_on_cancel=False``, the function ignores the cancellation and
       keeps going, just like if we had called ``sync_fn`` synchronously. This
       is the default behavior.
 
-    * If ``cancellable=True``, then this function immediately raises
+    * If ``abandon_on_cancel=True``, then this function immediately raises
       `~trio.Cancelled`. In this case **the thread keeps running in
       background** – we just abandon it to do whatever it's going to do, and
       silently discard any return value or errors that it raises. Only use
       this if you know that the operation is safe and side-effect free. (For
       example: :func:`trio.socket.getaddrinfo` uses a thread with
-      ``cancellable=True``, because it doesn't really affect anything if a
+      ``abandon_on_cancel=True``, because it doesn't really affect anything if a
       stray hostname lookup keeps running in the background.)
 
       The ``limiter`` is only released after the thread has *actually*
@@ -263,7 +287,20 @@ async def to_thread_run_sync(  # type: ignore[misc]
 
     """
     await trio.lowlevel.checkpoint_if_cancelled()
-    abandon_on_cancel = bool(cancellable)  # raise early if cancellable.__bool__ raises
+    if cancellable is not None:
+        if abandon_on_cancel is not None:
+            raise ValueError(
+                "Cannot set `cancellable` and `abandon_on_cancel` simultaneously."
+            )
+        warn_deprecated(
+            "The `cancellable=` keyword argument to `trio.to_thread.run_sync`",
+            "0.23.0",
+            issue=2841,
+            instead="`abandon_on_cancel=`",
+        )
+        abandon_on_cancel = cancellable
+    # raise early if abandon_on_cancel.__bool__ raises
+    abandon_on_cancel = bool(abandon_on_cancel)
     if limiter is None:
         limiter = current_default_thread_limiter()
 
@@ -381,14 +418,14 @@ def from_thread_check_cancelled() -> None:
     """Raise `trio.Cancelled` if the associated Trio task entered a cancelled status.
 
      Only applicable to threads spawned by `trio.to_thread.run_sync`. Poll to allow
-     ``cancellable=False`` threads to raise :exc:`~trio.Cancelled` at a suitable
-     place, or to end abandoned ``cancellable=True`` threads sooner than they may
+     ``abandon_on_cancel=False`` threads to raise :exc:`~trio.Cancelled` at a suitable
+     place, or to end abandoned ``abandon_on_cancel=True`` threads sooner than they may
      otherwise.
 
     Raises:
         Cancelled: If the corresponding call to `trio.to_thread.run_sync` has had a
             delivery of cancellation attempted against it, regardless of the value of
-            ``cancellable`` supplied as an argument to it.
+            ``abandon_on_cancel`` supplied as an argument to it.
         RuntimeError: If this thread is not spawned from `trio.to_thread.run_sync`.
 
     .. note::
diff --git a/trio/_wait_for_object.py b/trio/_wait_for_object.py
index d2193d9c86..53832513a3 100644
--- a/trio/_wait_for_object.py
+++ b/trio/_wait_for_object.py
@@ -45,7 +45,7 @@ async def WaitForSingleObject(obj: int | CData) -> None:
             WaitForMultipleObjects_sync,
             handle,
             cancel_handle,
-            cancellable=True,
+            abandon_on_cancel=True,
             limiter=trio.CapacityLimiter(math.inf),
         )
     finally: