diff --git a/doc/api/next_api_changes/deprecations/22317-AL.rst b/doc/api/next_api_changes/deprecations/22317-AL.rst
@@ -3,6 +3,6 @@ seaborn styles renamed
 Matplotlib currently ships many style files inspired from the seaborn
 library ("seaborn", "seaborn-bright", "seaborn-colorblind", etc.) but they
 have gone out of sync with the library itself since the release of seaborn
-0.9.  To prevent confusion, the style files have been renamed "seaborn0.8",
-"seaborn0.8-bright", "seaborn0.8-colorblind", etc.  Users are encouraged to
+0.9.  To prevent confusion, the style files have been renamed "seaborn-v0_8",
+"seaborn-v0_8-bright", "seaborn-v0_8-colorblind", etc.  Users are encouraged to
 directly use seaborn to access the up-to-date styles.
diff --git a/...-data/stylelib/seaborn0.8-bright.mplstyle → ...ata/stylelib/seaborn-v0_8-bright.mplstyle b/...-data/stylelib/seaborn0.8-bright.mplstyle → ...ata/stylelib/seaborn-v0_8-bright.mplstyle
diff --git a/...a/stylelib/seaborn0.8-colorblind.mplstyle → ...stylelib/seaborn-v0_8-colorblind.mplstyle b/...a/stylelib/seaborn0.8-colorblind.mplstyle → ...stylelib/seaborn-v0_8-colorblind.mplstyle
diff --git a/...stylelib/seaborn0.8-dark-palette.mplstyle → ...ylelib/seaborn-v0_8-dark-palette.mplstyle b/...stylelib/seaborn0.8-dark-palette.mplstyle → ...ylelib/seaborn-v0_8-dark-palette.mplstyle
diff --git a/...pl-data/stylelib/seaborn0.8-dark.mplstyle → ...-data/stylelib/seaborn-v0_8-dark.mplstyle b/...pl-data/stylelib/seaborn0.8-dark.mplstyle → ...-data/stylelib/seaborn-v0_8-dark.mplstyle
diff --git a/...ata/stylelib/seaborn0.8-darkgrid.mplstyle → ...a/stylelib/seaborn-v0_8-darkgrid.mplstyle b/...ata/stylelib/seaborn0.8-darkgrid.mplstyle → ...a/stylelib/seaborn-v0_8-darkgrid.mplstyle
diff --git a/...pl-data/stylelib/seaborn0.8-deep.mplstyle → ...-data/stylelib/seaborn-v0_8-deep.mplstyle b/...pl-data/stylelib/seaborn0.8-deep.mplstyle → ...-data/stylelib/seaborn-v0_8-deep.mplstyle
diff --git a/...l-data/stylelib/seaborn0.8-muted.mplstyle → ...data/stylelib/seaborn-v0_8-muted.mplstyle b/...l-data/stylelib/seaborn0.8-muted.mplstyle → ...data/stylelib/seaborn-v0_8-muted.mplstyle
diff --git a/...ata/stylelib/seaborn0.8-notebook.mplstyle → ...a/stylelib/seaborn-v0_8-notebook.mplstyle b/...ata/stylelib/seaborn0.8-notebook.mplstyle → ...a/stylelib/seaborn-v0_8-notebook.mplstyle
diff --git a/...l-data/stylelib/seaborn0.8-paper.mplstyle → ...data/stylelib/seaborn-v0_8-paper.mplstyle b/...l-data/stylelib/seaborn0.8-paper.mplstyle → ...data/stylelib/seaborn-v0_8-paper.mplstyle
diff --git a/...-data/stylelib/seaborn0.8-pastel.mplstyle → ...ata/stylelib/seaborn-v0_8-pastel.mplstyle b/...-data/stylelib/seaborn0.8-pastel.mplstyle → ...ata/stylelib/seaborn-v0_8-pastel.mplstyle
diff --git a/...-data/stylelib/seaborn0.8-poster.mplstyle → ...ata/stylelib/seaborn-v0_8-poster.mplstyle b/...-data/stylelib/seaborn0.8-poster.mplstyle → ...ata/stylelib/seaborn-v0_8-poster.mplstyle
diff --git a/...pl-data/stylelib/seaborn0.8-talk.mplstyle → ...-data/stylelib/seaborn-v0_8-talk.mplstyle b/...pl-data/stylelib/seaborn0.8-talk.mplstyle → ...-data/stylelib/seaborn-v0_8-talk.mplstyle
diff --git a/...l-data/stylelib/seaborn0.8-ticks.mplstyle → ...data/stylelib/seaborn-v0_8-ticks.mplstyle b/...l-data/stylelib/seaborn0.8-ticks.mplstyle → ...data/stylelib/seaborn-v0_8-ticks.mplstyle
diff --git a/...l-data/stylelib/seaborn0.8-white.mplstyle → ...data/stylelib/seaborn-v0_8-white.mplstyle b/...l-data/stylelib/seaborn0.8-white.mplstyle → ...data/stylelib/seaborn-v0_8-white.mplstyle
diff --git a/...ta/stylelib/seaborn0.8-whitegrid.mplstyle → .../stylelib/seaborn-v0_8-whitegrid.mplstyle b/...ta/stylelib/seaborn0.8-whitegrid.mplstyle → .../stylelib/seaborn-v0_8-whitegrid.mplstyle
diff --git a/...lib/mpl-data/stylelib/seaborn0.8.mplstyle → ...b/mpl-data/stylelib/seaborn-v0_8.mplstyle b/...lib/mpl-data/stylelib/seaborn0.8.mplstyle → ...b/mpl-data/stylelib/seaborn-v0_8.mplstyle
diff --git a/lib/matplotlib/style/core.py b/lib/matplotlib/style/core.py
@@ -135,9 +135,9 @@ def fix_style(s):
                     "3.6", message="The seaborn styles shipped by Matplotlib "
                     "are deprecated since %(since)s, as they no longer "
                     "correspond to the styles shipped by seaborn. However, "
-                    "they will remain available as 'seaborn0.8-<style>'. "
+                    "they will remain available as 'seaborn-v0_8-<style>'. "
                     "Alternatively, directly use the seaborn API instead.")
-                s = s.replace("seaborn", "seaborn0.8")
+                s = s.replace("seaborn", "seaborn-v0_8")
         return s
 
     for style in map(fix_style, styles):

diff --git a/lib/matplotlib/tests/test_style.py b/lib/matplotlib/tests/test_style.py
@@ -178,7 +178,7 @@ def test_xkcd_cm():
 
 
 def test_deprecated_seaborn_styles():
-    with mpl.style.context("seaborn0.8-bright"):
+    with mpl.style.context("seaborn-v0_8-bright"):
         seaborn_bright = mpl.rcParams.copy()
     assert mpl.rcParams != seaborn_bright
     with pytest.warns(mpl._api.MatplotlibDeprecationWarning):

diff --git a/tutorials/colors/colors.py b/tutorials/colors/colors.py
@@ -134,7 +134,7 @@ def demo(sty):
 
 
 demo('default')
-demo('seaborn0.8')
+demo('seaborn-v0_8')
 
 ###############################################################################
 # The first color ``'C0'`` is the title. Each plot uses the second and third