diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 812ea366b704a..4bb1e9efffff6 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -229,6 +229,9 @@ Other API Changes
 ^^^^^^^^^^^^^^^^^
 
 - :class:`DatetimeIndex` now accepts :class:`Int64Index` arguments as epoch timestamps (:issue:`20997`)
+- Accessing a level of a ``MultiIndex`` with a duplicate name (e.g. in
+  :meth:~MultiIndex.get_level_values) now raises a ``ValueError`` instead of
+  a ``KeyError`` (:issue:`21678`).
 - Invalid construction of ``IntervalDtype`` will now always raise a ``TypeError`` rather than a ``ValueError`` if the subdtype is invalid (:issue:`21185`)
 - Trying to reindex a ``DataFrame`` with a non unique ``MultiIndex`` now raises a ``ValueError`` instead of an ``Exception`` (:issue:`21770`)
 -
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index e143e5fdebfb1..b3bf7abe97279 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -19,6 +19,7 @@
     is_categorical_dtype,
     is_object_dtype,
     is_hashable,
+    is_integer,
     is_iterator,
     is_list_like,
     pandas_dtype,
@@ -757,14 +758,14 @@ def _from_elements(values, labels=None, levels=None, names=None,
         return MultiIndex(levels, labels, names, sortorder=sortorder)
 
     def _get_level_number(self, level):
+        count = self.names.count(level)
+        if (count > 1) and not is_integer(level):
+            raise ValueError('The name %s occurs multiple times, use a '
+                             'level number' % level)
         try:
-            count = self.names.count(level)
-            if count > 1:
-                raise ValueError('The name %s occurs multiple times, use a '
-                                 'level number' % level)
             level = self.names.index(level)
         except ValueError:
-            if not isinstance(level, int):
+            if not is_integer(level):
                 raise KeyError('Level %s not found' % str(level))
             elif level < 0:
                 level += self.nlevels
@@ -2879,13 +2880,6 @@ def isin(self, values, level=None):
             else:
                 return np.lib.arraysetops.in1d(labs, sought_labels)
 
-    def _reference_duplicate_name(self, name):
-        """
-        Returns True if the name refered to in self.names is duplicated.
-        """
-        # count the times name equals an element in self.names.
-        return sum(name == n for n in self.names) > 1
-
 
 MultiIndex._add_numeric_methods_disabled()
 MultiIndex._add_numeric_methods_add_sub_disabled()
diff --git a/pandas/core/reshape/reshape.py b/pandas/core/reshape/reshape.py
index 089634fb8e315..d5d2e594b8d6b 100644
--- a/pandas/core/reshape/reshape.py
+++ b/pandas/core/reshape/reshape.py
@@ -114,12 +114,6 @@ def __init__(self, values, index, level=-1, value_columns=None,
 
         self.index = index.remove_unused_levels()
 
-        if isinstance(self.index, MultiIndex):
-            if index._reference_duplicate_name(level):
-                msg = ("Ambiguous reference to {level}. The index "
-                       "names are not unique.".format(level=level))
-                raise ValueError(msg)
-
         self.level = self.index._get_level_number(level)
 
         # when index includes `nan`, need to lift levels/strides by 1
@@ -533,12 +527,6 @@ def factorize(index):
 
     N, K = frame.shape
 
-    if isinstance(frame.columns, MultiIndex):
-        if frame.columns._reference_duplicate_name(level):
-            msg = ("Ambiguous reference to {level}. The column "
-                   "names are not unique.".format(level=level))
-            raise ValueError(msg)
-
     # Will also convert negative level numbers and check if out of bounds.
     level_num = frame.columns._get_level_number(level)
 
diff --git a/pandas/tests/indexes/multi/test_unique_and_duplicates.py b/pandas/tests/indexes/multi/test_unique_and_duplicates.py
index a97d84ace9602..c1000e5b6e0f6 100644
--- a/pandas/tests/indexes/multi/test_unique_and_duplicates.py
+++ b/pandas/tests/indexes/multi/test_unique_and_duplicates.py
@@ -255,5 +255,5 @@ def test_unique_na():
 
 def test_duplicate_level_names_access_raises(idx):
     idx.names = ['foo', 'foo']
-    tm.assert_raises_regex(KeyError, 'Level foo not found',
+    tm.assert_raises_regex(ValueError, 'name foo occurs multiple times',
                            idx._get_level_number, 'foo')