diff --git a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/CompleteNextDataSetVersionImportFunctionTests.cs b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/CompleteNextDataSetVersionImportFunctionTests.cs
index 2e3101f0b5e..b8c131e3498 100644
--- a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/CompleteNextDataSetVersionImportFunctionTests.cs
+++ b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/CompleteNextDataSetVersionImportFunctionTests.cs
@@ -1,5 +1,6 @@
 using GovUk.Education.ExploreEducationStatistics.Common.Extensions;
 using GovUk.Education.ExploreEducationStatistics.Common.Tests.Extensions;
+using GovUk.Education.ExploreEducationStatistics.Common.Utils;
 using GovUk.Education.ExploreEducationStatistics.Content.Model;
 using GovUk.Education.ExploreEducationStatistics.Content.Model.Database;
 using GovUk.Education.ExploreEducationStatistics.Content.Model.Tests.Fixtures;
@@ -30,6 +31,17 @@ public class CompleteNextDataSetVersionImportTests(
         ProcessorFunctionsIntegrationTestFixture fixture)
         : CompleteNextDataSetVersionImportFunctionTests(fixture)
     {
+        public static TheoryData<DataSetVersionStatus> NonMappingDataSetVersionStatuses =
+            new(EnumUtil
+                .GetEnums<DataSetVersionStatus>()
+                .Except([DataSetVersionStatus.Mapping]));
+        
+        public static TheoryData<DataSetVersionImportStage> NonManualMappingStages =
+            new(EnumUtil
+                .GetEnums<DataSetVersionImportStage>()
+                .Except([DataSetVersionImportStage.ManualMapping]));
+
+        
         [Fact]
         public async Task Success()
         {
@@ -42,7 +54,7 @@ public async Task Success()
             durableTaskClientMock.Setup(client =>
                     client.ScheduleNewOrchestrationInstanceAsync(
                         nameof(ProcessCompletionOfNextDataSetVersionFunction
-                            .CompleteNextDataSetVersionImportProcessing),
+                            .ProcessCompletionOfNextDataSetVersion),
                         It.IsAny<ProcessDataSetVersionContext>(),
                         It.IsAny<StartOrchestrationOptions>(),
                         It.IsAny<CancellationToken>()))
@@ -71,6 +83,9 @@ public async Task Success()
 
             var responseViewModel = result.AssertOkObjectResult<ProcessDataSetVersionResponseViewModel>();
 
+            Assert.Equal(nextVersion.Id, responseViewModel.DataSetVersionId);
+            Assert.Equal(nextVersion.DataSetId, responseViewModel.DataSetId);
+
             // Assert that the pre-existing import entry for the next data set version is re-used.
             var updatedDataSetVersionImport = publicDataDbContext
                 .DataSetVersionImports
@@ -119,8 +134,10 @@ public async Task DataSetVersionIsNotFound_ReturnsNotFound()
                 expectedPath: nameof(NextDataSetVersionCompleteImportRequest.DataSetVersionId).ToLowerFirst());
         }
 
-        [Fact]
-        public async Task DataSetVersionNotInMappingStatus_ReturnsValidationProblem()
+        [Theory]
+        [MemberData(nameof(NonMappingDataSetVersionStatuses))]
+        public async Task DataSetVersionNotInMappingStatus_ReturnsValidationProblem(
+            DataSetVersionStatus status)
         {
             var (_, _, nextVersion) = await AddDataSetAndLatestLiveAndNextVersion();
 
@@ -131,7 +148,7 @@ public async Task DataSetVersionNotInMappingStatus_ReturnsValidationProblem()
                 .DataSetVersions
                 .SingleAsync(dsv => dsv.Id == nextVersion.Id);
 
-            nextVersionWithIncorrectStatus.Status = DataSetVersionStatus.Draft;
+            nextVersionWithIncorrectStatus.Status = status;
 
             await publicDataDbContext.SaveChangesAsync();
 
@@ -221,8 +238,10 @@ public async Task DataSetVersionMappings_FilterOptionsNotComplete_ReturnsValidat
                 expectedCode: ValidationMessages.DataSetVersionMappingsNotComplete.Code);
         }
 
-        [Fact]
-        public async Task DataSetVersionImportInManualMappingStateNotFound_ReturnsValidationProblem()
+        [Theory]
+        [MemberData(nameof(NonManualMappingStages))]
+        public async Task DataSetVersionImportInManualMappingStateNotFound_ReturnsValidationProblem(
+            DataSetVersionImportStage importStage)
         {
             var (_, _, nextVersion) = await AddDataSetAndLatestLiveAndNextVersion();
 
@@ -233,7 +252,7 @@ public async Task DataSetVersionImportInManualMappingStateNotFound_ReturnsValida
                 .DataSetVersionImports
                 .SingleAsync(import => import.DataSetVersionId == nextVersion.Id);
 
-            importWithIncorrectStatus.Stage = DataSetVersionImportStage.AutoMapping;
+            importWithIncorrectStatus.Stage = importStage;
 
             await publicDataDbContext.SaveChangesAsync();
 
diff --git a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/ProcessCompletionOfNextDataSetVersionImportFunctionTests.cs b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/ProcessCompletionOfNextDataSetVersionImportFunctionTests.cs
index b42d74762ee..5b6d2f69bb9 100644
--- a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/ProcessCompletionOfNextDataSetVersionImportFunctionTests.cs
+++ b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor.Tests/Functions/ProcessCompletionOfNextDataSetVersionImportFunctionTests.cs
@@ -124,7 +124,7 @@ private static Mock<TaskOrchestrationContext> DefaultMockOrchestrationContext(
         }
     }
 
-    public class CompleteInitialDataSetVersionProcessingTests(
+    public class CompleteNextDataSetVersionImportProcessingTests(
         ProcessorFunctionsIntegrationTestFixture fixture)
         : ProcessCompletionOfNextDataSetVersionImportFunctionTests(fixture)
     {
@@ -177,8 +177,8 @@ public async Task DuckDbFileIsDeleted()
 
         private async Task CompleteProcessing(Guid instanceId)
         {
-            var function = GetRequiredService<ProcessInitialDataSetVersionFunction>();
-            await function.CompleteInitialDataSetVersionProcessing(instanceId, CancellationToken.None);
+            var function = GetRequiredService<ProcessCompletionOfNextDataSetVersionFunction>();
+            await function.CompleteNextDataSetVersionImportProcessing(instanceId, CancellationToken.None);
         }
     }
 }
diff --git a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor/Functions/CompleteNextDataSetVersionImportFunction.cs b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor/Functions/CompleteNextDataSetVersionImportFunction.cs
index 90a2ef34fd4..283c1eb9db1 100644
--- a/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor/Functions/CompleteNextDataSetVersionImportFunction.cs
+++ b/src/GovUk.Education.ExploreEducationStatistics.Public.Data.Processor/Functions/CompleteNextDataSetVersionImportFunction.cs
@@ -143,7 +143,7 @@ private async Task ProcessCompletionOfNextDataSetVersionImport(
         CancellationToken cancellationToken)
     {
         const string orchestratorName =
-            nameof(ProcessCompletionOfNextDataSetVersionFunction.CompleteNextDataSetVersionImportProcessing);
+            nameof(ProcessCompletionOfNextDataSetVersionFunction.ProcessCompletionOfNextDataSetVersion);
 
         var input = new ProcessDataSetVersionContext { DataSetVersionId = dataSetVersionId };