BUG: remove single quotes in index names when printing

pandas/core/indexes/frozen.py

@@ -110,7 +110,11 @@ def _disabled(self, *args, **kwargs) -> NoReturn:
         raise TypeError(f"'{type(self).__name__}' does not support mutable operations.")
 
     def __str__(self) -> str:
-        return pprint_thing(self, quote_strings=True, escape_chars=("\t", "\r", "\n"))
+        return pprint_thing(
+            self,
+            quote_strings=True,
+            escape_chars=("\t", "\r", "\n", "'")
+        )
 
     def __repr__(self) -> str:
         return f"{type(self).__name__}({self!s})"

pandas/io/formats/printing.py

@@ -199,11 +199,10 @@ def pprint_thing(
     -------
     str
     """
-
     def as_escaped_string(
         thing: Any, escape_chars: EscapeChars | None = escape_chars
     ) -> str:
-        translate = {"\t": r"\t", "\n": r"\n", "\r": r"\r"}
+        translate = {"\t": r"\t", "\n": r"\n", "\r": r"\r", "'": r"\'"}
         if isinstance(escape_chars, Mapping):
             if default_escapes:
                 translate.update(escape_chars)

pandas/tests/io/formats/test_printing.py

@@ -2,12 +2,29 @@
 # functions, not the general printing of pandas objects.
 from collections.abc import Mapping
 import string
-
+import pytest
 import pandas._config.config as cf
-
+import pandas as pd
 from pandas.io.formats import printing
 
 
+@pytest.mark.parametrize("input_names, expected_names", [
+    (["'a", "b"], ["\'a", "b"]),             # Escape leading quote
+    (["test's", "b"], ["test\'s", "b"]),     # Escape apostrophe
+    (["'test'", "b"], ["\'test\'", "b"]),    # Escape surrounding quotes
+    (["test","b'"], ["test","b\'"]),         # Escape single quote
+    (["'test\n'", "b"], ["\'test\n\'", "b"]) # Escape and preserve newline
+])
+def test_formatted_index_names(input_names, expected_names):
+    # Create DataFrame with specified index names
+    df = pd.DataFrame(
+        {name: [1, 2, 3] for name in input_names}
+        ).set_index(input_names)
+    formatted_names = df.index.names
+
+    assert formatted_names == expected_names
+
+
 def test_adjoin():
     data = [["a", "b", "c"], ["dd", "ee", "ff"], ["ggg", "hhh", "iii"]]
     expected = "a  dd  ggg\nb  ee  hhh\nc  ff  iii"