diff --git a/prometheus_client/metrics.py b/prometheus_client/metrics.py
index dfa158b9..01b07e58 100644
--- a/prometheus_client/metrics.py
+++ b/prometheus_client/metrics.py
@@ -761,6 +761,7 @@ class Enum(MetricWrapperBase):
         e.state('running')
 
      The first listed state will be the default.
+     The full metric name, including namespace and subsystem, is reserved as a label name.
      Enum metrics do not work in multiprocess mode.
     """
     _type = 'stateset'
@@ -776,7 +777,7 @@ def __init__(self,
                  _labelvalues: Optional[Sequence[str]] = None,
                  states: Optional[Sequence[str]] = None,
                  ):
-        if name in labelnames:
+        if name in labelnames or _build_full_name(self._type, name, namespace, subsystem, unit) in labelnames:
             raise ValueError(f'Overlapping labels for Enum metric: {name}')
         if not states:
             raise ValueError(f'No states provided for Enum metric: {name}')
diff --git a/tests/test_core.py b/tests/test_core.py
index 2c29f79a..8f0174da 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -609,6 +609,23 @@ def test_failed_init_does_not_pollute_registry(self):
         Enum('task_state', 'help', states=['a', 'b'], registry=registry)
         self.assertEqual(1, registry.get_sample_value('task_state', {'task_state': 'a'}))
 
+    def test_prefixed_name_does_not_overlap_labels(self):
+        for namespace, subsystem in [('app', ''), ('', 'worker'), ('app', 'worker')]:
+            with self.subTest(namespace=namespace, subsystem=subsystem):
+                registry = CollectorRegistry()
+                name = '_'.join(part for part in (namespace, subsystem, 'state') if part)
+                with self.assertRaisesRegex(ValueError, 'Overlapping labels'):
+                    Enum('state', 'help', namespace=namespace, subsystem=subsystem,
+                         labelnames=[name], states=['a', 'b'], registry=registry)
+                self.assertEqual([], list(registry.collect()))
+
+                metric = Enum('state', 'help', namespace=namespace, subsystem=subsystem,
+                              labelnames=['tenant'], states=['a', 'b'], registry=registry)
+                metric.labels('one').state('a')
+                metric.labels('two').state('b')
+                self.assertEqual(1, registry.get_sample_value(name, {'tenant': 'one', name: 'a'}))
+                self.assertEqual(1, registry.get_sample_value(name, {'tenant': 'two', name: 'b'}))
+
 
 class TestMetricWrapper(unittest.TestCase):
     def setUp(self):