diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index df7a5dc9dc173..6cd2a91e9c17d 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -2298,7 +2298,28 @@ def levels(self):
 
     @property
     def names(self):
-        return [ping.name for ping in self.groupings]
+        # add suffix to level name in case they contain duplicates (GH 19029):
+        orig_names = [ping.name for ping in self.groupings]
+        # if no names were assigned return the original names
+        if all(x is None for x in orig_names):
+            return orig_names
+
+        suffixes = collections.defaultdict(int)
+        dups = {n: count for n, count in
+                collections.Counter(orig_names).items() if count > 1}
+        new_names = []
+        for name in orig_names:
+            if name not in dups:
+                new_names.append(name)
+            else:
+                if name is not None:
+                    new_name = '{0}_{1}'.format(name, suffixes[name])
+                else:
+                    new_name = '{0}'.format(suffixes[name])
+                suffixes[name] += 1
+                new_names.append(new_name)
+
+        return new_names
 
     def size(self):
         """
diff --git a/pandas/tests/groupby/test_categorical.py b/pandas/tests/groupby/test_categorical.py
index e0793b8e1bd64..fc3f2b1b7c4b7 100644
--- a/pandas/tests/groupby/test_categorical.py
+++ b/pandas/tests/groupby/test_categorical.py
@@ -558,10 +558,6 @@ def test_as_index():
     result = df.groupby(['cat', s], as_index=False, observed=True).sum()
     tm.assert_frame_equal(result, expected)
 
-    # GH18872: conflicting names in desired index
-    with pytest.raises(ValueError):
-        df.groupby(['cat', s.rename('cat')], observed=True).sum()
-
     # is original index dropped?
     group_columns = ['cat', 'A']
     expected = DataFrame(
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index e05f9de5ea7f4..a583c1230bfa4 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -1674,3 +1674,44 @@ def test_tuple_correct_keyerror():
                                                           [3, 4]]))
     with tm.assert_raises_regex(KeyError, "(7, 8)"):
         df.groupby((7, 8)).mean()
+
+
+def test_dup_index_names():
+    # dup. index names in groupby operations should be renamed (GH 19029):
+    df = pd.DataFrame({'date': pd.date_range('5.1.2018', '5.3.2018'),
+                       'vals': list(range(3))})
+
+    # duplicates get suffixed by integer position
+    mi = pd.MultiIndex.from_product([[5], [1, 2, 3]],
+                                    names=['date_0', 'date_1'])
+    expected = pd.Series(data=list(range(3)), index=mi, name='vals')
+    result = df.groupby([df.date.dt.month, df.date.dt.day])['vals'].sum()
+
+    tm.assert_series_equal(result, expected)
+
+    # 2 out of 3 are duplicates and None
+    mi = pd.MultiIndex.from_product([[2018], [5], [1, 2, 3]],
+                                    names=['0', '1', 'date'])
+    expected = pd.Series(data=list(range(3)), index=mi, name='vals')
+    result = df.groupby([df.date.dt.year.rename(None),
+                         df.date.dt.month.rename(None),
+                         df.date.dt.day])['vals'].sum()
+    tm.assert_series_equal(result, expected)
+
+    # 2 out of 3 names (not None) are duplicates, the remaining is None
+    mi = pd.MultiIndex.from_product([[2018], [5], [1, 2, 3]],
+                                    names=['date_0', None, 'date_1'])
+    expected = pd.Series(data=list(range(3)), index=mi, name='vals')
+    result = df.groupby([df.date.dt.year,
+                         df.date.dt.month.rename(None),
+                         df.date.dt.day])['vals'].sum()
+    tm.assert_series_equal(result, expected)
+
+    # all are None
+    mi = pd.MultiIndex.from_product([[2018], [5], [1, 2, 3]],
+                                    names=[None, None, None])
+    expected = pd.Series(data=list(range(3)), index=mi, name='vals')
+    result = df.groupby([df.date.dt.year.rename(None),
+                         df.date.dt.month.rename(None),
+                         df.date.dt.day.rename(None)])['vals'].sum()
+    tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index d2cf3fc11e165..3e416e6fed161 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -1705,9 +1705,21 @@ def test_crosstab_with_numpy_size(self):
         tm.assert_frame_equal(result, expected)
 
     def test_crosstab_dup_index_names(self):
-        # GH 13279, GH 18872
+        # duplicated index name should get renamed (GH 19029)
         s = pd.Series(range(3), name='foo')
-        pytest.raises(ValueError, pd.crosstab, s, s)
+        failed = False
+        try:
+            result = pd.crosstab(s, s)
+        except ValueError:
+            failed = True
+
+        assert failed is False
+
+        s0 = pd.Series(range(3), name='foo0')
+        s1 = pd.Series(range(3), name='foo1')
+        expected = pd.DataFrame(np.diag(np.ones(3, dtype='int64')),
+                                index=s0, columns=s1)
+        tm.assert_frame_equal(result, expected)
 
     @pytest.mark.parametrize("names", [['a', ('b', 'c')],
                                        [('a', 'b'), 'c']])