diff --git a/cinder/backup/manager.py b/cinder/backup/manager.py
index 1110cebdb76..55b4d998a0d 100644
--- a/cinder/backup/manager.py
+++ b/cinder/backup/manager.py
@@ -521,11 +521,13 @@ class BackupManager(manager.ThreadPoolManager):
         if not backup:
             return True
 
-        # TODO(tommylikehu): We upgraded the 'driver_name' from module
-        # to class name, so we use 'in' here to match two namings,
-        # this can be replaced with equal sign during next
-        # release (Rocky).
-        if self.driver_name.startswith(backup):
+        # TODO(tommylikehu): We upgraded the 'driver_name' from module to
+        # class name, so we use 'startswith' here to match two namings,
+        # this can be replaced with equal sign during next release (Rocky).
+        # The 'driver_name' varies depending on the user settings, so a
+        # two-way judgment is required.
+        if self.driver_name.startswith(backup) or backup.startswith(
+                self.driver_name):
             return True
 
         # We support renaming of drivers, so check old names as well
diff --git a/cinder/tests/unit/backup/test_backup.py b/cinder/tests/unit/backup/test_backup.py
index b5df7fd908c..8628e2c6386 100644
--- a/cinder/tests/unit/backup/test_backup.py
+++ b/cinder/tests/unit/backup/test_backup.py
@@ -1778,6 +1778,29 @@ class BackupTestCase(BaseBackupTest):
         self.assertEqual(100, tpool._nthreads)
         self.assertListEqual([], tpool._threads)
 
+    def test_driver_name_startswith_backup_service_name(self):
+        service_name = 'cinder.tests.unit.backup.fake_service'
+        driver_name = 'cinder.tests.unit.backup.fake_service.FakeBackupService'
+        self.override_config('backup_driver', driver_name)
+        vol_id = self._create_volume_db_entry(status='available', size=1)
+        backup = self._create_backup_db_entry(status=fields.BackupStatus.ERROR,
+                                              volume_id=vol_id,
+                                              service=service_name)
+        result = self.backup_mgr._is_our_backup(backup)
+        self.assertTrue(result)
+
+    def test_backup_service_name_startswith_driver_name(self):
+        driver_name = 'cinder.tests.unit.backup.fake_service'
+        service_name = ('cinder.tests.unit.backup.fake_service.'
+                        'FakeBackupService')
+        self.override_config('backup_driver', driver_name)
+        vol_id = self._create_volume_db_entry(status='available', size=1)
+        backup = self._create_backup_db_entry(status=fields.BackupStatus.ERROR,
+                                              volume_id=vol_id,
+                                              service=service_name)
+        result = self.backup_mgr._is_our_backup(backup)
+        self.assertTrue(result)
+
 
 class BackupTestCaseWithVerify(BaseBackupTest):
     """Test Case for backups."""