diff --git a/doc/source/whatsnew/v0.17.0.txt b/doc/source/whatsnew/v0.17.0.txt
index ad3b966575427..00290bb9a1484 100644
--- a/doc/source/whatsnew/v0.17.0.txt
+++ b/doc/source/whatsnew/v0.17.0.txt
@@ -464,6 +464,8 @@ Performance Improvements
 Bug Fixes
 ~~~~~~~~~
 
+
+- Bug in ``DataFrame.to_html(index=False)`` renders unnecessary ``name`` row (:issue:`10344`)
 - Bug in ``DataFrame.apply`` when function returns categorical series. (:issue:`9573`)
 - Bug in ``to_datetime`` with invalid dates and formats supplied (:issue:`10154`)
 - Bug in ``Index.drop_duplicates`` dropping name(s) (:issue:`10115`)
diff --git a/pandas/core/format.py b/pandas/core/format.py
index 6a05f819908af..81d47d9e1f36c 100644
--- a/pandas/core/format.py
+++ b/pandas/core/format.py
@@ -1037,7 +1037,7 @@ def _column_header():
             self.write_tr(col_row, indent, self.indent_delta, header=True,
                           align=align)
 
-        if self.fmt.has_index_names:
+        if self.fmt.has_index_names and self.fmt.index:
             row = [
                 x if x is not None else '' for x in self.frame.index.names
             ] + [''] * min(len(self.columns), self.max_cols)
diff --git a/pandas/tests/test_format.py b/pandas/tests/test_format.py
index b733cacc01e05..5af12070f5a2d 100644
--- a/pandas/tests/test_format.py
+++ b/pandas/tests/test_format.py
@@ -632,6 +632,10 @@ def test_to_html_multiindex_index_false(self):
 </table>"""
         self.assertEqual(result, expected)
 
+        df.index = Index(df.index.values, name='idx')
+        result = df.to_html(index=False)
+        self.assertEqual(result, expected)
+
     def test_to_html_multiindex_sparsify_false_multi_sparse(self):
         with option_context('display.multi_sparse', False):
             index = MultiIndex.from_arrays([[0, 0, 1, 1], [0, 1, 0, 1]],
@@ -1922,15 +1926,195 @@ def test_to_html_index(self):
                            'C': ['one', 'two', np.NaN]},
                           columns=['A', 'B', 'C'],
                           index=index)
+        expected_with_index = ('<table border="1" class="dataframe">\n'
+                               '  <thead>\n'
+                               '    <tr style="text-align: right;">\n'
+                               '      <th></th>\n'
+                               '      <th>A</th>\n'
+                               '      <th>B</th>\n'
+                               '      <th>C</th>\n'
+                               '    </tr>\n'
+                               '  </thead>\n'
+                               '  <tbody>\n'
+                               '    <tr>\n'
+                               '      <th>foo</th>\n'
+                               '      <td>1</td>\n'
+                               '      <td>1.2</td>\n'
+                               '      <td>one</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bar</th>\n'
+                               '      <td>2</td>\n'
+                               '      <td>3.4</td>\n'
+                               '      <td>two</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>baz</th>\n'
+                               '      <td>3</td>\n'
+                               '      <td>5.6</td>\n'
+                               '      <td>NaN</td>\n'
+                               '    </tr>\n'
+                               '  </tbody>\n'
+                               '</table>')
+        self.assertEqual(df.to_html(), expected_with_index)
+
+        expected_without_index = ('<table border="1" class="dataframe">\n'
+                                  '  <thead>\n'
+                                  '    <tr style="text-align: right;">\n'
+                                  '      <th>A</th>\n'
+                                  '      <th>B</th>\n'
+                                  '      <th>C</th>\n'
+                                  '    </tr>\n'
+                                  '  </thead>\n'
+                                  '  <tbody>\n'
+                                  '    <tr>\n'
+                                  '      <td>1</td>\n'
+                                  '      <td>1.2</td>\n'
+                                  '      <td>one</td>\n'
+                                  '    </tr>\n'
+                                  '    <tr>\n'
+                                  '      <td>2</td>\n'
+                                  '      <td>3.4</td>\n'
+                                  '      <td>two</td>\n'
+                                  '    </tr>\n'
+                                  '    <tr>\n'
+                                  '      <td>3</td>\n'
+                                  '      <td>5.6</td>\n'
+                                  '      <td>NaN</td>\n'
+                                  '    </tr>\n'
+                                  '  </tbody>\n'
+                                  '</table>')
         result = df.to_html(index=False)
         for i in index:
             self.assertNotIn(i, result)
+        self.assertEqual(result, expected_without_index)
+        df.index = Index(['foo', 'bar', 'baz'], name='idx')
+        expected_with_index = ('<table border="1" class="dataframe">\n'
+                               '  <thead>\n'
+                               '    <tr style="text-align: right;">\n'
+                               '      <th></th>\n'
+                               '      <th>A</th>\n'
+                               '      <th>B</th>\n'
+                               '      <th>C</th>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>idx</th>\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '    </tr>\n'
+                               '  </thead>\n'
+                               '  <tbody>\n'
+                               '    <tr>\n'
+                               '      <th>foo</th>\n'
+                               '      <td>1</td>\n'
+                               '      <td>1.2</td>\n'
+                               '      <td>one</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bar</th>\n'
+                               '      <td>2</td>\n'
+                               '      <td>3.4</td>\n'
+                               '      <td>two</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>baz</th>\n'
+                               '      <td>3</td>\n'
+                               '      <td>5.6</td>\n'
+                               '      <td>NaN</td>\n'
+                               '    </tr>\n'
+                               '  </tbody>\n'
+                               '</table>')
+        self.assertEqual(df.to_html(), expected_with_index)
+        self.assertEqual(df.to_html(index=False), expected_without_index)
 
         tuples = [('foo', 'car'), ('foo', 'bike'), ('bar', 'car')]
         df.index = MultiIndex.from_tuples(tuples)
+
+        expected_with_index = ('<table border="1" class="dataframe">\n'
+                               '  <thead>\n'
+                               '    <tr style="text-align: right;">\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '      <th>A</th>\n'
+                               '      <th>B</th>\n'
+                               '      <th>C</th>\n'
+                               '    </tr>\n'
+                               '  </thead>\n'
+                               '  <tbody>\n'
+                               '    <tr>\n'
+                               '      <th rowspan="2" valign="top">foo</th>\n'
+                               '      <th>car</th>\n'
+                               '      <td>1</td>\n'
+                               '      <td>1.2</td>\n'
+                               '      <td>one</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bike</th>\n'
+                               '      <td>2</td>\n'
+                               '      <td>3.4</td>\n'
+                               '      <td>two</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bar</th>\n'
+                               '      <th>car</th>\n'
+                               '      <td>3</td>\n'
+                               '      <td>5.6</td>\n'
+                               '      <td>NaN</td>\n'
+                               '    </tr>\n'
+                               '  </tbody>\n'
+                               '</table>')
+        self.assertEqual(df.to_html(), expected_with_index)
+
         result = df.to_html(index=False)
         for i in ['foo', 'bar', 'car', 'bike']:
             self.assertNotIn(i, result)
+        # must be the same result as normal index
+        self.assertEqual(result, expected_without_index)
+
+        df.index = MultiIndex.from_tuples(tuples, names=['idx1', 'idx2'])
+        expected_with_index = ('<table border="1" class="dataframe">\n'
+                               '  <thead>\n'
+                               '    <tr style="text-align: right;">\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '      <th>A</th>\n'
+                               '      <th>B</th>\n'
+                               '      <th>C</th>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>idx1</th>\n'
+                               '      <th>idx2</th>\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '      <th></th>\n'
+                               '    </tr>\n'
+                               '  </thead>\n'
+                               '  <tbody>\n'
+                               '    <tr>\n'
+                               '      <th rowspan="2" valign="top">foo</th>\n'
+                               '      <th>car</th>\n'
+                               '      <td>1</td>\n'
+                               '      <td>1.2</td>\n'
+                               '      <td>one</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bike</th>\n'
+                               '      <td>2</td>\n'
+                               '      <td>3.4</td>\n'
+                               '      <td>two</td>\n'
+                               '    </tr>\n'
+                               '    <tr>\n'
+                               '      <th>bar</th>\n'
+                               '      <th>car</th>\n'
+                               '      <td>3</td>\n'
+                               '      <td>5.6</td>\n'
+                               '      <td>NaN</td>\n'
+                               '    </tr>\n'
+                               '  </tbody>\n'
+                               '</table>')
+        self.assertEqual(df.to_html(), expected_with_index)
+        self.assertEqual(df.to_html(index=False), expected_without_index)
 
     def test_repr_html(self):
         self.frame._repr_html_()