diff --git a/tensorflow/python/eager/def_function.py b/tensorflow/python/eager/def_function.py
index a150baafd60..9b46001506b 100644
--- a/tensorflow/python/eager/def_function.py
+++ b/tensorflow/python/eager/def_function.py
@@ -316,12 +316,16 @@ class Function(object):
         return weak_wrapped_fn().__wrapped__(*args, **kwds)
     weak_wrapped_fn = weakref.ref(wrapped_fn)
 
+    return self._defun(tf_decorator.make_decorator(
+        self._python_function,
+        wrapped_fn,
+        decorator_argspec=self._function_spec.fullargspec))
+
+  def _defun(self, fn):
+    """Returns a defun generated from the input function."""
     # TODO(mdan): Pipe self._experimental_autograph_options through.
     return function_lib.defun(
-        tf_decorator.make_decorator(
-            self._python_function,
-            wrapped_fn,
-            decorator_argspec=self._function_spec.fullargspec),
+        fn,
         input_signature=self.input_signature,
         autograph=self._autograph,
         experimental_autograph_options=self._experimental_autograph_options)
diff --git a/tensorflow/python/training/training_util.py b/tensorflow/python/training/training_util.py
index 86f1b4d5aae..d526a17297f 100644
--- a/tensorflow/python/training/training_util.py
+++ b/tensorflow/python/training/training_util.py
@@ -230,7 +230,7 @@ def _get_or_create_global_step_read(graph=None):
     return None
   # add 'zero' so that it will create a copy of variable as Tensor.
   with graph.as_default() as g, g.name_scope(None):
-    with g.name_scope(global_step_tensor.op.name + '/'):
+    with g.name_scope(global_step_tensor._shared_name + '/'):  # pylint: disable=protected-access
       # using initialized_value to ensure that global_step is initialized before
       # this run. This is needed for example Estimator makes all model_fn build
       # under global_step_read_tensor dependency.
@@ -242,6 +242,7 @@ def _get_or_create_global_step_read(graph=None):
 
 
 def _increment_global_step(increment, graph=None):
+  """Increments the global step variable."""
   graph = graph or ops.get_default_graph()
   global_step_tensor = get_global_step(graph)
   if global_step_tensor is None:
@@ -250,6 +251,6 @@ def _increment_global_step(increment, graph=None):
         'tf.train.get_or_create_global_step before calling increment.')
   global_step_read_tensor = _get_or_create_global_step_read(graph)
   with graph.as_default() as g, g.name_scope(None):
-    with g.name_scope(global_step_tensor.op.name + '/'):
+    with g.name_scope(global_step_tensor._shared_name + '/'):  # pylint: disable=protected-access
       with ops.control_dependencies([global_step_read_tensor]):
         return state_ops.assign_add(global_step_tensor, increment)