diff --git a/doc/source/whatsnew/v0.17.0.txt b/doc/source/whatsnew/v0.17.0.txt
index d59b6120163ff..3c89bb3b78c07 100644
--- a/doc/source/whatsnew/v0.17.0.txt
+++ b/doc/source/whatsnew/v0.17.0.txt
@@ -348,8 +348,7 @@ Bug Fixes
 - Bug in ``ExcelReader`` when worksheet is empty (:issue:`6403`)
 - Bug in ``Table.select_column`` where name is not preserved (:issue:`10392`)
 - Bug in ``offsets.generate_range`` where ``start`` and ``end`` have finer precision than ``offset`` (:issue:`9907`)
-
-
+- Bug in ``pd.rolling_*`` where ``Series.name`` would be lost in the output (:issue:`10565`)
 
 
 
diff --git a/pandas/stats/moments.py b/pandas/stats/moments.py
index 41a768783b1cb..586d507b27493 100644
--- a/pandas/stats/moments.py
+++ b/pandas/stats/moments.py
@@ -426,7 +426,7 @@ def _process_data_structure(arg, kill_inf=True):
         values = arg.values
     elif isinstance(arg, Series):
         values = arg.values
-        return_hook = lambda v: Series(v, arg.index)
+        return_hook = lambda v: Series(v, arg.index, name=arg.name)
     else:
         return_hook = lambda v: v
         values = arg
diff --git a/pandas/stats/tests/test_moments.py b/pandas/stats/tests/test_moments.py
index a0e4d5663fde9..1741676abf773 100644
--- a/pandas/stats/tests/test_moments.py
+++ b/pandas/stats/tests/test_moments.py
@@ -725,6 +725,14 @@ def test_ewma_halflife_arg(self):
         self.assertRaises(Exception, mom.ewma, self.arr, com=9.5, span=20, halflife=50)
         self.assertRaises(Exception, mom.ewma, self.arr)
 
+    def test_moment_preserve_series_name(self):
+        # GH 10565
+        s = Series(np.arange(100), name='foo')
+        s2 = mom.rolling_mean(s, 30)
+        s3 = mom.rolling_sum(s, 20)
+        self.assertEqual(s2.name, 'foo')
+        self.assertEqual(s3.name, 'foo')
+
     def test_ew_empty_arrays(self):
         arr = np.array([], dtype=np.float64)