diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index d53de30187156..761149ee7bc63 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -338,7 +338,7 @@ Conversion
 - Bug in :class:`Series` floor-division where operating on a scalar ``timedelta`` raises an exception (:issue:`18846`)
 - Bug in :class:`FY5253Quarter`, :class:`LastWeekOfMonth` where rollback and rollforward behavior was inconsistent with addition and subtraction behavior (:issue:`18854`)
 - Bug in :class:`Index` constructor with ``dtype=CategoricalDtype(...)`` where ``categories`` and ``ordered`` are not maintained (issue:`19032`)
-- Bug in :class:`Index` constructor with ``dtype=CategoricalDtype(...)`` where ``categories`` and ``ordered`` are not maintained (issue:`19032`) 
+- Bug in :class:`Index` constructor with ``dtype=CategoricalDtype(...)`` where ``categories`` and ``ordered`` are not maintained (issue:`19032`)
 - Bug in :class:`Series`` with ``dtype='timedelta64[ns]`` where addition or subtraction of ``TimedeltaIndex`` had results cast to ``dtype='int64'`` (:issue:`17250`)
 - Bug in :class:`TimedeltaIndex` where division by a ``Series`` would return a ``TimedeltaIndex`` instead of a ``Series`` (issue:`19042`)
 - Bug in :class:`Series` with ``dtype='timedelta64[ns]`` where addition or subtraction of ``TimedeltaIndex`` could return a ``Series`` with an incorrect name (issue:`19043`)
@@ -364,6 +364,7 @@ Indexing
 - Bug in :func:`DatetimeIndex.insert` where inserting ``NaT`` into a timezone-aware index incorrectly raised (:issue:`16357`)
 - Bug in ``__setitem__`` when indexing a :class:`DataFrame` with a 2-d boolean ndarray (:issue:`18582`)
 - Bug in ``str.extractall`` when there were no matches empty :class:`Index` was returned instead of appropriate :class:`MultiIndex` (:issue:`19034`)
+- Bug in :func:`Index.__add__` would lose the index name after operations (:issue:`17067`)
 
 I/O
 ^^^
diff --git a/pandas/core/common.py b/pandas/core/common.py
index e606be3cc2a23..3e240ce383586 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -205,9 +205,9 @@ def is_bool_indexer(key):
     return False
 
 
-def _default_index(n):
+def _default_index(n, name=None):
     from pandas.core.index import RangeIndex
-    return RangeIndex(0, n, name=None)
+    return RangeIndex(0, n, name=name)
 
 
 def _mut_exclusive(**kwargs):
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 55a26d57fa1d6..bc0513c42e023 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2141,7 +2141,7 @@ def argsort(self, *args, **kwargs):
         return result.argsort(*args, **kwargs)
 
     def __add__(self, other):
-        return Index(np.array(self) + other)
+        return Index(np.array(self) + other, name=self.name)
 
     def __radd__(self, other):
         return Index(other + np.array(self))
diff --git a/pandas/tests/frame/test_alter_axes.py b/pandas/tests/frame/test_alter_axes.py
index c824f0026af50..891dde0975505 100644
--- a/pandas/tests/frame/test_alter_axes.py
+++ b/pandas/tests/frame/test_alter_axes.py
@@ -824,6 +824,11 @@ def test_reset_index_range(self):
                                 index=RangeIndex(stop=2))
         assert_frame_equal(result, expected)
 
+    def test_reset_index_name(self):
+        # issue `17067`: after reset_index, index name should be None
+        df = pd.DataFrame(index=pd.Index([], name='x'))
+        assert df.reset_index(level=[]).index.name is None
+
     def test_set_index_names(self):
         df = pd.util.testing.makeDataFrame()
         df.index.name = 'name'
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 5109542403b43..09cc38b40fc6d 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -957,6 +957,14 @@ def test_iadd_string(self):
         index += '_x'
         assert 'a_x' in index
 
+    def test_iadd_index_name(self):
+        # issue `17067`: test Index keeping index name after plus op
+        s = pd.Series([1, 2, 3])
+        s.index.name = 'foo'
+
+        s.index += 1
+        assert s.index.name == 'foo'
+
     def test_difference(self):
 
         first = self.strIndex[5:20]