diff --git a/xarray/core/combine.py b/xarray/core/combine.py
index 97c36c85a3c..ea2c6e89ec2 100644
--- a/xarray/core/combine.py
+++ b/xarray/core/combine.py
@@ -138,7 +138,7 @@ def _calc_concat_dim_coord(dim):
         coord = as_variable(dim).to_index_variable()
         dim, = coord.dims
     else:
-        coord = dim
+        coord = dim.rename({dim.dims[0]: dim.name})
         dim, = coord.dims
     return dim, coord
 
diff --git a/xarray/tests/test_combine.py b/xarray/tests/test_combine.py
index b2bbba34fef..ee5673f876f 100644
--- a/xarray/tests/test_combine.py
+++ b/xarray/tests/test_combine.py
@@ -234,6 +234,14 @@ def test_concat_multiindex(self):
         assert expected.equals(actual)
         assert isinstance(actual.x.to_index(), pd.MultiIndex)
 
+    def test_concat_dim_name(self):
+        da = [DataArray(np.random.randn(3), dims=['d1']) for aa in range(5)]
+        labels = ['foo1', 'foo2', 'foo3', 'foo4', 'foo5']
+        daconcat = concat(da, DataArray(labels, name='stat'))
+        pdconcat = concat(da, pd.Index(labels, name='stat'))
+
+        self.assertDataArrayEqual(daconcat, pdconcat)
+
 
 class TestConcatDataArray(TestCase):
     def test_concat(self):