diff --git a/pandas/io/formats/style.py b/pandas/io/formats/style.py
index 4fc13fd54df02..9e0769f22e102 100644
--- a/pandas/io/formats/style.py
+++ b/pandas/io/formats/style.py
@@ -1114,6 +1114,8 @@ def _copy(self, deepcopy: bool = False) -> Styler:
         shallow = [  # simple string or boolean immutables
             "hide_index_",
             "hide_columns_",
+            "hide_column_names",
+            "hide_index_names",
             "table_attributes",
             "cell_ids",
             "caption",
@@ -2024,6 +2026,7 @@ def hide_index(
         self,
         subset: Subset | None = None,
         level: Level | list[Level] | None = None,
+        names: bool = False,
     ) -> Styler:
         """
         Hide the entire index, or specific keys in the index from rendering.
@@ -2047,6 +2050,11 @@ def hide_index(
             The level(s) to hide in a MultiIndex if hiding the entire index. Cannot be
             used simultaneously with ``subset``.
 
+            .. versionadded:: 1.4.0
+        names : bool
+            Whether to hide the index name(s), in the case the index or part of it
+            remains visible.
+
             .. versionadded:: 1.4.0
 
         Returns
@@ -2100,7 +2108,7 @@ def hide_index(
 
         Hide a specific level:
 
-        >>> df.style.format("{:,.1f").hide_index(level=1)  # doctest: +SKIP
+        >>> df.style.format("{:,.1f}").hide_index(level=1)  # doctest: +SKIP
                              x                    y
                a      b      c      a      b      c
         x    0.1    0.0    0.4    1.3    0.6   -1.4
@@ -2109,11 +2117,29 @@ def hide_index(
         y    0.4    1.0   -0.2   -0.8   -1.2    1.1
             -0.6    1.2    1.8    1.9    0.3    0.3
              0.8    0.5   -0.3    1.2    2.2   -0.8
+
+        Hiding just the index level names:
+
+        >>> df.index.names = ["lev0", "lev1"]
+        >>> df.style.format("{:,.1f}").hide_index(names=True)  # doctest: +SKIP
+                                 x                    y
+                   a      b      c      a      b      c
+        x   a    0.1    0.0    0.4    1.3    0.6   -1.4
+            b    0.7    1.0    1.3    1.5   -0.0   -0.2
+            c    1.4   -0.8    1.6   -0.2   -0.4   -0.3
+        y   a    0.4    1.0   -0.2   -0.8   -1.2    1.1
+            b   -0.6    1.2    1.8    1.9    0.3    0.3
+            c    0.8    0.5   -0.3    1.2    2.2   -0.8
         """
         if level is not None and subset is not None:
             raise ValueError("`subset` and `level` cannot be passed simultaneously")
 
         if subset is None:
+            if level is None and names:
+                # this combination implies user shows the index and hides just names
+                self.hide_index_names = True
+                return self
+
             levels_ = _refactor_levels(level, self.index)
             self.hide_index_ = [
                 True if lev in levels_ else False for lev in range(self.index.nlevels)
@@ -2126,12 +2152,16 @@ def hide_index(
             # error: Incompatible types in assignment (expression has type
             # "ndarray", variable has type "Sequence[int]")
             self.hidden_rows = hrows  # type: ignore[assignment]
+
+        if names:
+            self.hide_index_names = True
         return self
 
     def hide_columns(
         self,
         subset: Subset | None = None,
         level: Level | list[Level] | None = None,
+        names: bool = False,
     ) -> Styler:
         """
         Hide the column headers or specific keys in the columns from rendering.
@@ -2155,6 +2185,11 @@ def hide_columns(
             The level(s) to hide in a MultiIndex if hiding the entire column headers
             row. Cannot be used simultaneously with ``subset``.
 
+            .. versionadded:: 1.4.0
+        names : bool
+            Whether to hide the column index name(s), in the case all column headers,
+            or some levels, are visible.
+
             .. versionadded:: 1.4.0
 
         Returns
@@ -2221,11 +2256,29 @@ def hide_columns(
         y   a    0.4    1.0   -0.2   -0.8   -1.2    1.1
             b   -0.6    1.2    1.8    1.9    0.3    0.3
             c    0.8    0.5   -0.3    1.2    2.2   -0.8
+
+        Hiding just the column level names:
+
+        >>> df.columns.names = ["lev0", "lev1"]
+        >>> df.style.format("{:.1f").hide_columns(names=True)  # doctest: +SKIP
+                   x                    y
+                   a      b      c      a      b      c
+        x   a    0.1    0.0    0.4    1.3    0.6   -1.4
+            b    0.7    1.0    1.3    1.5   -0.0   -0.2
+            c    1.4   -0.8    1.6   -0.2   -0.4   -0.3
+        y   a    0.4    1.0   -0.2   -0.8   -1.2    1.1
+            b   -0.6    1.2    1.8    1.9    0.3    0.3
+            c    0.8    0.5   -0.3    1.2    2.2   -0.8
         """
         if level is not None and subset is not None:
             raise ValueError("`subset` and `level` cannot be passed simultaneously")
 
         if subset is None:
+            if level is None and names:
+                # this combination implies user shows the column headers but hides names
+                self.hide_column_names = True
+                return self
+
             levels_ = _refactor_levels(level, self.columns)
             self.hide_columns_ = [
                 True if lev in levels_ else False for lev in range(self.columns.nlevels)
@@ -2238,6 +2291,9 @@ def hide_columns(
             # error: Incompatible types in assignment (expression has type
             # "ndarray", variable has type "Sequence[int]")
             self.hidden_columns = hcols  # type: ignore[assignment]
+
+        if names:
+            self.hide_column_names = True
         return self
 
     # -----------------------------------------------------------------------
diff --git a/pandas/io/formats/style_render.py b/pandas/io/formats/style_render.py
index f51a1f5d9809d..e94dc63530163 100644
--- a/pandas/io/formats/style_render.py
+++ b/pandas/io/formats/style_render.py
@@ -98,6 +98,8 @@ def __init__(
         self.cell_ids = cell_ids
 
         # add rendering variables
+        self.hide_index_names: bool = False
+        self.hide_column_names: bool = False
         self.hide_index_: list = [False] * self.index.nlevels
         self.hide_columns_: list = [False] * self.columns.nlevels
         self.hidden_rows: Sequence[int] = []  # sequence for specific hidden rows/cols
@@ -334,7 +336,9 @@ def _translate_header(
                     _element(
                         "th",
                         f"{blank_class if name is None else index_name_class} level{r}",
-                        name if name is not None else blank_value,
+                        name
+                        if (name is not None and not self.hide_column_names)
+                        else blank_value,
                         not all(self.hide_index_),
                     )
                 ]
@@ -383,6 +387,7 @@ def _translate_header(
             and com.any_not_none(*self.data.index.names)
             and not all(self.hide_index_)
             and not all(self.hide_columns_)
+            and not self.hide_index_names
         ):
             index_names = [
                 _element(
diff --git a/pandas/tests/io/formats/style/test_style.py b/pandas/tests/io/formats/style/test_style.py
index dc8be68532f0e..4fb8c90bbd77e 100644
--- a/pandas/tests/io/formats/style/test_style.py
+++ b/pandas/tests/io/formats/style/test_style.py
@@ -48,8 +48,10 @@ def mi_styler_comp(mi_styler):
     mi_styler.set_table_styles([{"selector": "a", "props": "a:v;"}])
     mi_styler.hide_columns()
     mi_styler.hide_columns([("c0", "c1_a")])
+    mi_styler.hide_columns(names=True)
     mi_styler.hide_index()
     mi_styler.hide_index([("i0", "i1_a")])
+    mi_styler.hide_index(names=True)
     mi_styler.set_table_attributes('class="box"')
     mi_styler.format(na_rep="MISSING", precision=3)
     mi_styler.highlight_max(axis=None)
@@ -239,6 +241,8 @@ def test_copy(comprehensive, render, deepcopy, mi_styler, mi_styler_comp):
             "cell_ids",
             "hide_index_",
             "hide_columns_",
+            "hide_index_names",
+            "hide_column_names",
             "table_attributes",
         ]
         for attr in shallow:
@@ -1398,3 +1402,40 @@ def test_non_reducing_multi_slice_on_multiindex(self, slice_):
         with tm.assert_produces_warning(warn, match=msg):
             result = df.loc[non_reducing_slice(slice_)]
         tm.assert_frame_equal(result, expected)
+
+
+def test_hidden_index_names(mi_df):
+    mi_df.index.names = ["Lev0", "Lev1"]
+    mi_styler = mi_df.style
+    ctx = mi_styler._translate(True, True)
+    assert len(ctx["head"]) == 3  # 2 column index levels + 1 index names row
+
+    mi_styler.hide_index(names=True)
+    ctx = mi_styler._translate(True, True)
+    assert len(ctx["head"]) == 2  # index names row is unparsed
+    for i in range(4):
+        assert ctx["body"][0][i]["is_visible"]  # 2 index levels + 2 data values visible
+
+    mi_styler.hide_index(level=1)
+    ctx = mi_styler._translate(True, True)
+    assert len(ctx["head"]) == 2  # index names row is still hidden
+    assert ctx["body"][0][0]["is_visible"] is True
+    assert ctx["body"][0][1]["is_visible"] is False
+
+
+def test_hidden_column_names(mi_df):
+    mi_df.columns.names = ["Lev0", "Lev1"]
+    mi_styler = mi_df.style
+    ctx = mi_styler._translate(True, True)
+    assert ctx["head"][0][1]["display_value"] == "Lev0"
+    assert ctx["head"][1][1]["display_value"] == "Lev1"
+
+    mi_styler.hide_columns(names=True)
+    ctx = mi_styler._translate(True, True)
+    assert ctx["head"][0][1]["display_value"] == " "
+    assert ctx["head"][1][1]["display_value"] == " "
+
+    mi_styler.hide_columns(level=0)
+    ctx = mi_styler._translate(True, True)
+    assert len(ctx["head"]) == 1  # no index names and only one visible column headers
+    assert ctx["head"][0][1]["display_value"] == " "