diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 884107d4bc6af..486a6a2a02be3 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -3568,6 +3568,7 @@ def _wrap(x, alt_format_):
         elif formatters is None and float_format is not None:
             formatters_ = partial(_wrap, alt_format_=lambda v: v)
         format_index_ = [index_format_, column_format_]
+        format_index_names_ = [index_format_, column_format_]
 
         # Deal with hiding indexes and relabelling column names
         hide_: list[dict] = []
@@ -3616,6 +3617,7 @@ def _wrap(x, alt_format_):
             relabel_index=relabel_index_,
             format={"formatter": formatters_, **base_format_},
             format_index=format_index_,
+            format_index_names=format_index_names_,
             render_kwargs=render_kwargs_,
         )
 
@@ -3628,6 +3630,7 @@ def _to_latex_via_styler(
         relabel_index: dict | list[dict] | None = None,
         format: dict | list[dict] | None = None,
         format_index: dict | list[dict] | None = None,
+        format_index_names: dict | list[dict] | None = None,
         render_kwargs: dict | None = None,
     ):
         """
@@ -3672,7 +3675,13 @@ def _to_latex_via_styler(
         self = cast("DataFrame", self)
         styler = Styler(self, uuid="")
 
-        for kw_name in ["hide", "relabel_index", "format", "format_index"]:
+        for kw_name in [
+            "hide",
+            "relabel_index",
+            "format",
+            "format_index",
+            "format_index_names",
+        ]:
             kw = vars()[kw_name]
             if isinstance(kw, dict):
                 getattr(styler, kw_name)(**kw)
diff --git a/pandas/tests/io/formats/test_to_latex.py b/pandas/tests/io/formats/test_to_latex.py
index 8d46442611719..ebc6ff5be108f 100644
--- a/pandas/tests/io/formats/test_to_latex.py
+++ b/pandas/tests/io/formats/test_to_latex.py
@@ -824,6 +824,46 @@ def test_to_latex_escape_special_chars(self):
         )
         assert result == expected
 
+    def test_to_latex_escape_special_chars_in_index_names(self):
+        # https://github.com/pandas-dev/pandas/issues/61309
+        # https://github.com/pandas-dev/pandas/issues/57362
+        index = "&%$#_{}}~^\\"
+        df = DataFrame({index: [1, 2, 3]}).set_index(index)
+        result = df.to_latex(escape=True)
+        expected = _dedent(
+            r"""
+            \begin{tabular}{l}
+            \toprule
+            \&\%\$\#\_\{\}\}\textasciitilde \textasciicircum \textbackslash  \\
+            \midrule
+            1 \\
+            2 \\
+            3 \\
+            \bottomrule
+            \end{tabular}
+            """
+        )
+        assert result == expected
+
+    def test_to_latex_escape_special_chars_in_column_name(self):
+        df = DataFrame({"A": [1, 2, 3], "B": ["a", "b", "c"]})
+        df.columns.name = "_^~"
+        result = df.to_latex(escape=True)
+        expected = _dedent(
+            r"""
+            \begin{tabular}{lrl}
+            \toprule
+            \_\textasciicircum \textasciitilde  & A & B \\
+            \midrule
+            0 & 1 & a \\
+            1 & 2 & b \\
+            2 & 3 & c \\
+            \bottomrule
+            \end{tabular}
+            """
+        )
+        assert result == expected
+
     def test_to_latex_specified_header_special_chars_without_escape(self):
         # GH 7124
         df = DataFrame({"a": [1, 2], "b": ["b1", "b2"]})