BUG: Fixed to_html ignoring index_names parameter

closes #16493

Author: Christian Prinoth <christian@prinoth.name>
Author: Tom Augspurger <tom.w.augspurger@gmail.com>
Author: Christian Prinoth <c.prinoth@CPmbpro.local>
Author: Jeff Reback <jeff.reback@twosigma.com>

This patch had conflicts when merged, resolved by
Committer: Jeff Reback <jeff.reback@twosigma.com>

Closes #16495 from CRP/bugfix_16493 and squashes the following commits:

567ae69 [Jeff Reback] doc corrections
8429f9a [Tom Augspurger] Fixed lint error
469a0e6 [Christian Prinoth] BUG: fix for bug 16493
20d512f [Christian Prinoth] BUG: fix for bug 16493
6bef829 [Christian Prinoth] BUG: fix for bug 16493
426565e [Christian Prinoth] BUG: fix for bug 16493
a40820d [Christian Prinoth] BUG: fix for bug 16493

(cherry picked from commit e3ee186)

Author: CRP

doc/source/whatsnew/v0.20.2.txt

@@ -64,6 +64,7 @@ I/O
 - 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 in ``pd.read_csv()`` in which tarfile object inputs were raising an error in Python 2.x for the C engine (:issue:`16530`)
+- Bug where ``DataFrame.to_html()`` ignored the ``index_names`` parameter (:issue:`16493`)
 
 
 Plotting

pandas/io/formats/format.py

@@ -1289,7 +1289,9 @@ 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