diff -Naur django-3.2.orig/django/utils/version.py django-3.2/django/utils/version.py
--- django-3.2.orig/django/utils/version.py	2021-04-06 17:27:22.000000000 +0800
+++ django-3.2/django/utils/version.py	2023-10-08 15:52:24.619595829 +0800
@@ -13,6 +13,8 @@
 PY37 = sys.version_info >= (3, 7)
 PY38 = sys.version_info >= (3, 8)
 PY39 = sys.version_info >= (3, 9)
+PY310 = sys.version_info >= (3, 10)
+PY311 = sys.version_info >= (3, 11)
 
 
 def get_version(version=None):
diff -Naur django-3.2.orig/tests/test_runner/test_debug_sql.py django-3.2/tests/test_runner/test_debug_sql.py
--- django-3.2.orig/tests/test_runner/test_debug_sql.py	2021-04-06 17:27:22.000000000 +0800
+++ django-3.2/tests/test_runner/test_debug_sql.py	2023-10-08 15:52:24.718595822 +0800
@@ -4,6 +4,7 @@
 from django.db import connection
 from django.test import TestCase
 from django.test.runner import DiscoverRunner
+from django.utils.version import PY311
 
 from .models import Person
 
@@ -100,14 +101,17 @@
             '''"test_runner_person"."first_name" = 'subtest-fail';'''),
     ]
 
+    # Python 3.11 uses fully qualified test name in the output.
+    method_name = ".runTest" if PY311 else ""
+    test_class_path = "test_runner.test_debug_sql.TestDebugSQL"
     verbose_expected_outputs = [
-        'runTest (test_runner.test_debug_sql.TestDebugSQL.FailingTest) ... FAIL',
-        'runTest (test_runner.test_debug_sql.TestDebugSQL.ErrorTest) ... ERROR',
-        'runTest (test_runner.test_debug_sql.TestDebugSQL.PassingTest) ... ok',
+        f"runTest ({test_class_path}.FailingTest{method_name}) ... FAIL",
+        f"runTest ({test_class_path}.ErrorTest{method_name}) ... ERROR",
+        f"runTest ({test_class_path}.PassingTest{method_name}) ... ok",
         # If there are errors/failures in subtests but not in test itself,
         # the status is not written. That behavior comes from Python.
-        'runTest (test_runner.test_debug_sql.TestDebugSQL.FailingSubTest) ...',
-        'runTest (test_runner.test_debug_sql.TestDebugSQL.ErrorSubTest) ...',
+        f"runTest ({test_class_path}.FailingSubTest{method_name}) ...",
+        f"runTest ({test_class_path}.ErrorSubTest{method_name}) ...",
         ('''SELECT COUNT(*) AS "__count" '''
             '''FROM "test_runner_person" WHERE '''
             '''"test_runner_person"."first_name" = 'pass';'''),
diff -Naur django-3.2.orig/tests/test_runner/test_parallel.py django-3.2/tests/test_runner/test_parallel.py
--- django-3.2.orig/tests/test_runner/test_parallel.py	2021-04-06 17:27:22.000000000 +0800
+++ django-3.2/tests/test_runner/test_parallel.py	2023-10-08 15:52:24.718595822 +0800
@@ -2,7 +2,7 @@
 
 from django.test import SimpleTestCase
 from django.test.runner import RemoteTestResult
-from django.utils.version import PY37
+from django.utils.version import PY37, PY311
 
 try:
     import tblib
@@ -79,7 +79,11 @@
 
         event = events[1]
         self.assertEqual(event[0], 'addSubTest')
-        self.assertEqual(str(event[2]), 'dummy_test (test_runner.test_parallel.SampleFailingSubtest) (index=0)')
+        self.assertEqual(str(event[2]),
+            "dummy_test (test_runner.test_parallel.SampleFailingSubtest%s) (index=0)"
+            # Python 3.11 uses fully qualified test name in the output.
+            % (".dummy_test" if PY311 else ""),
+        )
         trailing_comma = '' if PY37 else ','
         self.assertEqual(repr(event[3][1]), "AssertionError('0 != 1'%s)" % trailing_comma)
 
diff -Naur django-3.2.orig/tests/test_utils/tests.py django-3.2/tests/test_utils/tests.py
--- django-3.2.orig/tests/test_utils/tests.py	2021-04-06 17:27:22.000000000 +0800
+++ django-3.2/tests/test_utils/tests.py	2023-10-08 15:52:24.719595822 +0800
@@ -26,6 +26,7 @@
 )
 from django.urls import NoReverseMatch, path, reverse, reverse_lazy
 from django.utils.deprecation import RemovedInDjango41Warning
+from django.utils.version import PY311
 
 from .models import Car, Person, PossessedCar
 from .views import empty_response
@@ -78,9 +79,11 @@
             SkipTestCase('test_foo').test_foo,
             ValueError,
             "skipUnlessDBFeature cannot be used on test_foo (test_utils.tests."
-            "SkippingTestCase.test_skip_unless_db_feature.<locals>.SkipTestCase) "
+            "SkippingTestCase.test_skip_unless_db_feature.<locals>.SkipTestCase%s) "
             "as SkippingTestCase.test_skip_unless_db_feature.<locals>.SkipTestCase "
             "doesn't allow queries against the 'default' database."
+            # Python 3.11 uses fully qualified test name in the output.
+            % (".test_foo" if PY311 else ""),
         )
 
     def test_skip_if_db_feature(self):
@@ -122,9 +125,11 @@
             SkipTestCase('test_foo').test_foo,
             ValueError,
             "skipIfDBFeature cannot be used on test_foo (test_utils.tests."
-            "SkippingTestCase.test_skip_if_db_feature.<locals>.SkipTestCase) "
+            "SkippingTestCase.test_skip_if_db_feature.<locals>.SkipTestCase%s) "
             "as SkippingTestCase.test_skip_if_db_feature.<locals>.SkipTestCase "
             "doesn't allow queries against the 'default' database."
+            # Python 3.11 uses fully qualified test name in the output.
+            % (".test_foo" if PY311 else ""),
         )