Fixed to_html ignoring index_names parameter

doc/source/whatsnew/v0.20.2.txt

@@ -59,6 +59,7 @@ I/O
 - Bug in pd.read_csv() when comment is passed in space deliminted text files (:issue:`16472`)
 - Bug that would force importing of the clipboard routines unnecessarily, potentially causing an import error on startup (:issue:`16288`)
 - Bug that raised IndexError HTML-rendering an empty DataFrame (:issue:`15953`)
+- Bug where ``DataFrame.to_html()`` ignored the ``index_names`` parameter (:issue:`16493`)
 
 
 Plotting

pandas/io/formats/format.py

@@ -1292,7 +1292,9 @@ def _column_header():
             self.write_tr(col_row, indent, self.indent_delta, header=True,
                           align=align)
 
-        if self.fmt.has_index_names and self.fmt.index:
+        if all((self.fmt.has_index_names,
+                self.fmt.index,
+                self.fmt.show_index_names)):
             row = ([x if x is not None else ''
                     for x in self.frame.index.names] +
                    [''] * min(len(self.columns), self.max_cols))

pandas/tests/io/formats/test_to_html.py

@@ -1869,3 +1869,10 @@ def test_to_html_notebook_has_no_style(self):
         df = pd.DataFrame({"A": [1, 2, 3]})
         result = df.to_html()
         assert "thead tr:only-child" not in result
+
+    def test_to_html_with_index_names_false(self):
+        # gh-16493
+        df = pd.DataFrame({"A": [1, 2]}, index=pd.Index(['a', 'b'],
+                                                        name='myindexname'))
+        result = df.to_html(index_names=False)
+        assert 'myindexname' not in result