diff --git a/newsfragments/4434.bugfix.rst b/newsfragments/4434.bugfix.rst
new file mode 100644
index 0000000000..5eeb674297
--- /dev/null
+++ b/newsfragments/4434.bugfix.rst
@@ -0,0 +1,2 @@
+Fix distribution name normalisation (:pep:`625`) for valid versions that are
+not canonical (e.g. ``1.0-2``).
diff --git a/setuptools/_core_metadata.py b/setuptools/_core_metadata.py
index f1de9c9ba6..45aae7d70b 100644
--- a/setuptools/_core_metadata.py
+++ b/setuptools/_core_metadata.py
@@ -18,7 +18,7 @@
 from . import _normalization, _reqs
 from .extern.packaging.markers import Marker
 from .extern.packaging.requirements import Requirement
-from .extern.packaging.utils import canonicalize_name
+from .extern.packaging.utils import canonicalize_name, canonicalize_version
 from .extern.packaging.version import Version
 from .warnings import SetuptoolsDeprecationWarning
 
@@ -263,7 +263,23 @@ def _write_provides_extra(file, processed_extras, safe, unsafe):
 
 # from pypa/distutils#244; needed only until that logic is always available
 def get_fullname(self):
+    return _distribution_fullname(self.get_name(), self.get_version())
+
+
+def _distribution_fullname(name: str, version: str) -> str:
+    """
+    >>> _distribution_fullname('setup.tools', '1.0-2')
+    'setup_tools-1.0.post2'
+    >>> _distribution_fullname('setup-tools', '1.2post2')
+    'setup_tools-1.2.post2'
+    >>> _distribution_fullname('setup-tools', '1.0-r2')
+    'setup_tools-1.0.post2'
+    >>> _distribution_fullname('setup.tools', '1.0.post')
+    'setup_tools-1.0.post0'
+    >>> _distribution_fullname('setup.tools', '1.0+ubuntu-1')
+    'setup_tools-1.0+ubuntu.1'
+    """
     return "{}-{}".format(
-        canonicalize_name(self.get_name()).replace('-', '_'),
-        self.get_version(),
+        canonicalize_name(name).replace('-', '_'),
+        canonicalize_version(version, strip_trailing_zero=False),
     )