diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index a5949c62ad913..907c91a742573 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -113,14 +113,18 @@ class Index(IndexOpsMixin, PandasObject):
     dtype : NumPy dtype (default: object)
     copy : bool
         Make a copy of input ndarray
-    name : object
+    name : object, optional
         Name to be stored in the index
+    names : sequence of objects, optional
+        Names for the index levels
     tupleize_cols : bool (default: True)
         When True, attempt to create a MultiIndex if possible
 
     Notes
     -----
-    An Index instance can **only** contain hashable objects
+    An Index instance can **only** contain hashable objects.
+
+    Only one of `name` and `names` can be specified at the same time.
 
     Examples
     --------
@@ -176,10 +180,25 @@ class Index(IndexOpsMixin, PandasObject):
     str = CachedAccessor("str", StringMethods)
 
     def __new__(cls, data=None, dtype=None, copy=False, name=None,
-                fastpath=False, tupleize_cols=True, **kwargs):
+                fastpath=False, tupleize_cols=True, names=None,
+                **kwargs):
+
+        # The main purpose of `names` is to use it with a `MultiIndex`.
+        # Although for consistency it's also used to retrieve `name` for a
+        # one-level indices if `name` is not provided (see GH 19082).
+
+        if names is not None and name is not None:
+            raise TypeError("Can provide only one of names and name arguments")
+
+        if names is not None and not is_list_like(names):
+            raise TypeError("names must be list-like")
 
-        if name is None and hasattr(data, 'name'):
-            name = data.name
+        if name is None:
+            if hasattr(data, 'name'):
+                name = data.name
+            # extract `name` from `names` in case MultiIndex cannot be created
+            elif names:
+                name = names[0]
 
         if fastpath:
             return cls._simple_new(data, name)
@@ -358,8 +377,7 @@ def __new__(cls, data=None, dtype=None, copy=False, name=None,
                 # 10697
                 if all(isinstance(e, tuple) for e in data):
                     from .multi import MultiIndex
-                    return MultiIndex.from_tuples(
-                        data, names=name or kwargs.get('names'))
+                    return MultiIndex.from_tuples(data, names=names or name)
             # other iterable of some kind
             subarr = _asarray_tuplesafe(data, dtype=object)
             return Index(subarr, dtype=dtype, copy=copy, name=name, **kwargs)
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index c4e8682934369..d7247669ea43b 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -305,6 +305,30 @@ def test_constructor_simple_new(self):
         result = idx._simple_new(idx, 'obj')
         tm.assert_index_equal(result, idx)
 
+    def test_constructor_names(self):
+        # test both `name` and `names` provided
+        with pytest.raises(TypeError):
+            idx = Index([1, 2, 3], name='a', names=('a',))
+
+        # test non-list-like `names`
+        with pytest.raises(TypeError):
+            idx = Index([1, 2, 3], names='a')
+
+        # test using `name` for a flat `Index`
+        idx = Index([1, 2, 3], name='a')
+        assert idx.name == 'a'
+        assert idx.names == ('a',)
+
+        # test using `names` for a flat `Index`
+        idx = Index([1, 2, 3], names=('a',))
+        assert idx.name == 'a'
+        assert idx.names == ('a',)
+
+        # test using `names` for `MultiIndex` creation
+        idx = Index([('A', 1), ('A', 2)], names=('a', 'b'))
+        midx = MultiIndex.from_tuples([('A', 1), ('A', 2)], names=('a', 'b'))
+        tm.assert_index_equal(idx, midx, check_names=True)
+
     def test_constructor_dtypes(self):
 
         for idx in [Index(np.array([1, 2, 3], dtype=int)),