diff --git a/doc/source/categorical.rst b/doc/source/categorical.rst
index 8835c4a1533d0..65361886436d6 100644
--- a/doc/source/categorical.rst
+++ b/doc/source/categorical.rst
@@ -146,6 +146,8 @@ Using ``.describe()`` on categorical data will produce similar output to a `Seri
     df.describe()
     df["cat"].describe()
 
+.. _categorical.cat:
+
 Working with categories
 -----------------------
 
diff --git a/doc/source/whatsnew/v0.21.0.txt b/doc/source/whatsnew/v0.21.0.txt
index 52e056103cbdc..d192166f620f2 100644
--- a/doc/source/whatsnew/v0.21.0.txt
+++ b/doc/source/whatsnew/v0.21.0.txt
@@ -566,6 +566,7 @@ Categorical
 - Bug in the categorical constructor with empty values and categories causing
   the ``.categories`` to be an empty ``Float64Index`` rather than an empty
   ``Index`` with object dtype (:issue:`17248`)
+- Bug in categorical operations with :ref:`Series.cat <categorical.cat>' not preserving the original Series' name (:issue:`17509`)
 
 PyPy
 ^^^^
diff --git a/pandas/core/categorical.py b/pandas/core/categorical.py
index e67ce2936819f..ddca93f07ad5e 100644
--- a/pandas/core/categorical.py
+++ b/pandas/core/categorical.py
@@ -2054,9 +2054,10 @@ class CategoricalAccessor(PandasDelegate, NoNewAttributesMixin):
 
     """
 
-    def __init__(self, values, index):
+    def __init__(self, values, index, name):
         self.categorical = values
         self.index = index
+        self.name = name
         self._freeze()
 
     def _delegate_property_get(self, name):
@@ -2075,14 +2076,15 @@ def _delegate_method(self, name, *args, **kwargs):
         method = getattr(self.categorical, name)
         res = method(*args, **kwargs)
         if res is not None:
-            return Series(res, index=self.index)
+            return Series(res, index=self.index, name=self.name)
 
     @classmethod
     def _make_accessor(cls, data):
         if not is_categorical_dtype(data.dtype):
             raise AttributeError("Can only use .cat accessor with a "
                                  "'category' dtype")
-        return CategoricalAccessor(data.values, data.index)
+        return CategoricalAccessor(data.values, data.index,
+                                   getattr(data, 'name', None),)
 
 
 CategoricalAccessor._add_delegate_accessors(delegate=Categorical,
diff --git a/pandas/tests/test_categorical.py b/pandas/tests/test_categorical.py
index 1fa3c84dc0260..c361b430cfd8a 100644
--- a/pandas/tests/test_categorical.py
+++ b/pandas/tests/test_categorical.py
@@ -57,6 +57,25 @@ def test_getitem_listlike(self):
         expected = c[np.array([100000]).astype(np.int64)].codes
         tm.assert_numpy_array_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "method",
+        [
+            lambda x: x.cat.set_categories([1, 2, 3]),
+            lambda x: x.cat.reorder_categories([2, 3, 1], ordered=True),
+            lambda x: x.cat.rename_categories([1, 2, 3]),
+            lambda x: x.cat.remove_unused_categories(),
+            lambda x: x.cat.remove_categories([2]),
+            lambda x: x.cat.add_categories([4]),
+            lambda x: x.cat.as_ordered(),
+            lambda x: x.cat.as_unordered(),
+        ])
+    def test_getname_categorical_accessor(self, method):
+        # GH 17509
+        s = pd.Series([1, 2, 3], name='A').astype('category')
+        expected = 'A'
+        result = method(s).name
+        assert result == expected
+
     def test_getitem_category_type(self):
         # GH 14580
         # test iloc() on Series with Categorical data