diff --git a/pandas/core/index.py b/pandas/core/index.py
index fd11cd7f598c3..e2dd996bd133f 100644
--- a/pandas/core/index.py
+++ b/pandas/core/index.py
@@ -976,7 +976,9 @@ def append(self, other):
             to_concat.append(other)
 
         for obj in to_concat:
-            if isinstance(obj, Index) and obj.name != name:
+            if (isinstance(obj, Index) and
+                obj.name != name and
+                obj.name is not None):
                 name = None
                 break
 
diff --git a/pandas/tests/test_index.py b/pandas/tests/test_index.py
index bb75b12754dca..e378e2ed4b93f 100644
--- a/pandas/tests/test_index.py
+++ b/pandas/tests/test_index.py
@@ -4075,6 +4075,19 @@ def test_groupby(self):
         exp = dict((key, [key]) for key in self.index)
         tm.assert_dict_equal(groups, exp)
 
+    def test_index_name_retained(self):
+        # GH9857
+        result = pd.DataFrame({'x': [1, 2, 6],
+                               'y': [2, 2, 8],
+                               'z': [-5, 0, 5]})
+        result = result.set_index('z')
+        result.loc[10] = [9, 10]
+        df_expected = pd.DataFrame({'x': [1, 2, 6, 9],
+                                    'y': [2, 2, 8, 10],
+                                    'z': [-5, 0, 5, 10]})
+        df_expected = df_expected.set_index('z')
+        tm.assert_frame_equal(result, df_expected)
+
 
 def test_get_combined_index():
     from pandas.core.index import _get_combined_index