diff --git a/doc/source/whatsnew/v0.18.0.txt b/doc/source/whatsnew/v0.18.0.txt
index 5b8c282d3e4ed..ea5c3b6e4c7d0 100644
--- a/doc/source/whatsnew/v0.18.0.txt
+++ b/doc/source/whatsnew/v0.18.0.txt
@@ -238,4 +238,6 @@ Bug Fixes
 
 - Bug in ``df.replace`` while replacing value in mixed dtype ``Dataframe`` (:issue:`11698`)
 
+- Bug in ``Index`` prevent copying name of passed ``Index`` or ``DatetimeIndex`` objects, when a new name is not provided (:issue:`11193`)
+
 - Bug in ``read_excel`` failing to read any non-empty sheets when empty sheets exist and ``sheetname=None`` (:issue:`11711`)
diff --git a/pandas/core/index.py b/pandas/core/index.py
index 9b75153d9b84b..6da30ffefb41f 100644
--- a/pandas/core/index.py
+++ b/pandas/core/index.py
@@ -120,6 +120,9 @@ class Index(IndexOpsMixin, StringAccessorMixin, PandasObject):
     def __new__(cls, data=None, dtype=None, copy=False, name=None, fastpath=False,
                 tupleize_cols=True, **kwargs):
 
+        if name is None and hasattr(data, 'name'):
+            name = data.name
+
         # no class inference!
         if fastpath:
             return cls._simple_new(data, name)
@@ -128,6 +131,7 @@ def __new__(cls, data=None, dtype=None, copy=False, name=None, fastpath=False,
             return CategoricalIndex(data, copy=copy, name=name, **kwargs)
 
         if isinstance(data, (np.ndarray, Index, ABCSeries)):
+
             if issubclass(data.dtype.type, np.datetime64) or is_datetimetz(data):
                 from pandas.tseries.index import DatetimeIndex
                 result = DatetimeIndex(data, copy=copy, name=name, **kwargs)
@@ -4052,6 +4056,8 @@ def __new__(cls, levels=None, labels=None, sortorder=None, names=None,
         # compat with Index
         if name is not None:
             names = name
+#        elif cls.names is not None:
+#            names = cls.names
         if levels is None or labels is None:
             raise TypeError("Must pass both levels and labels")
         if len(levels) != len(labels):
diff --git a/pandas/tests/test_base.py b/pandas/tests/test_base.py
index 5d959892791fe..db391dca7114c 100644
--- a/pandas/tests/test_base.py
+++ b/pandas/tests/test_base.py
@@ -415,6 +415,7 @@ def test_value_counts_unique_nunique(self):
 
                 # resets name from Index
                 expected_index = pd.Index(o[::-1])
+                expected_index.name = None
 
                 # attach name to klass
                 o = o.repeat(range(1, len(o) + 1))
@@ -424,16 +425,18 @@ def test_value_counts_unique_nunique(self):
 
                 # resets name from Index
                 expected_index = pd.Index(o[::-1])
+                expected_index.name = None
 
                 # attach name to klass
                 o = o.repeat(range(1, len(o) + 1))
                 o.name = 'a'
 
             # don't test boolean
-            elif isinstance(o,Index) and o.is_boolean():
+            elif isinstance(o, Index) and o.is_boolean():
                 continue
             elif isinstance(o, Index):
                 expected_index = pd.Index(values[::-1])
+                expected_index.name = None
                 o = o.repeat(range(1, len(o) + 1))
                 o.name = 'a'
             else:
diff --git a/pandas/tests/test_index.py b/pandas/tests/test_index.py
index e2fa6a90429dc..a240b8c1c1e78 100644
--- a/pandas/tests/test_index.py
+++ b/pandas/tests/test_index.py
@@ -60,6 +60,31 @@ def test_shift(self):
         self.assertRaises(NotImplementedError, idx.shift, 1)
         self.assertRaises(NotImplementedError, idx.shift, 1, 2)
 
+    def test_create_index_existing_name(self):
+
+        # GH11193, when an existing index is passed, and a new name is not specified, the new index should inherit the
+        # previous object name
+        expected = self.create_index()
+        if not isinstance(expected, MultiIndex):
+            expected.name = 'foo'
+            result = pd.Index(expected)
+            tm.assert_index_equal(result, expected)
+
+            result = pd.Index(expected, name='bar')
+            expected.name = 'bar'
+            tm.assert_index_equal(result, expected)
+        else:
+            expected.names = ['foo', 'bar']
+            result = pd.Index(expected)
+            tm.assert_index_equal(result, Index(Index([('foo', 'one'), ('foo', 'two'), ('bar', 'one'), ('baz', 'two'),
+                                                       ('qux', 'one'), ('qux', 'two')], dtype='object'),
+                                                names=['foo', 'bar']))
+
+            result = pd.Index(expected, names=['A', 'B'])
+            tm.assert_index_equal(result, Index(Index([('foo', 'one'), ('foo', 'two'), ('bar', 'one'), ('baz', 'two'),
+                                                       ('qux', 'one'), ('qux', 'two')], dtype='object'),
+                                                names=['A', 'B']))
+
     def test_numeric_compat(self):
 
         idx = self.create_index()
@@ -3043,7 +3068,7 @@ def test_identical(self):
         i = self.index.copy(dtype=object)
         i = i.rename('foo')
         same_values = Index(i, dtype=object)
-        self.assertTrue(same_values.identical(self.index.copy(dtype=object)))
+        self.assertTrue(same_values.identical(i))
 
         self.assertFalse(i.identical(self.index))
         self.assertTrue(Index(same_values, name='foo', dtype=object