diff --git a/lib/matplotlib/_mathtext.py b/lib/matplotlib/_mathtext.py
index bbb247ec02fe..73e6163944e1 100644
--- a/lib/matplotlib/_mathtext.py
+++ b/lib/matplotlib/_mathtext.py
@@ -264,7 +264,7 @@ def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
         if bunch is not None:
             return bunch
 
-        font, num, symbol_name, fontsize, slanted = \
+        font, num, glyph_name, fontsize, slanted = \
             self._get_glyph(fontname, font_class, sym, fontsize, math)
 
         font.set_size(fontsize, dpi)
@@ -292,7 +292,8 @@ def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
             fontsize        = fontsize,
             postscript_name = font.postscript_name,
             metrics         = metrics,
-            symbol_name     = symbol_name,
+            glyph_name      = glyph_name,
+            symbol_name     = glyph_name,  # Backcompat alias.
             num             = num,
             glyph           = glyph,
             offset          = offset
@@ -358,7 +359,7 @@ def __init__(self, *args, **kwargs):
     _slanted_symbols = set(r"\int \oint".split())
 
     def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
-        symbol_name = None
+        glyph_name = None
         font = None
         if fontname in self.fontmap and sym in latex_to_bakoma:
             basename, num = latex_to_bakoma[sym]
@@ -373,13 +374,13 @@ def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
         if font is not None:
             gid = font.get_char_index(num)
             if gid != 0:
-                symbol_name = font.get_glyph_name(gid)
+                glyph_name = font.get_glyph_name(gid)
 
-        if symbol_name is None:
+        if glyph_name is None:
             return self._stix_fallback._get_glyph(
                 fontname, font_class, sym, fontsize, math)
 
-        return font, num, symbol_name, fontsize, slanted
+        return font, num, glyph_name, fontsize, slanted
 
     # The Bakoma fonts contain many pre-sized alternatives for the
     # delimiters.  The AutoSizedChar class will use these alternatives
@@ -556,8 +557,8 @@ def _get_glyph(self, fontname, font_class, sym, fontsize, math=True):
                 glyphindex = font.get_char_index(uniindex)
                 slanted = False
 
-        symbol_name = font.get_glyph_name(glyphindex)
-        return font, uniindex, symbol_name, fontsize, slanted
+        glyph_name = font.get_glyph_name(glyphindex)
+        return font, uniindex, glyph_name, fontsize, slanted
 
     def get_sized_alternatives_for_symbol(self, fontname, sym):
         if self.cm_fallback:
@@ -854,7 +855,7 @@ def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
 
         if found_symbol:
             try:
-                symbol_name = font.get_name_char(glyph)
+                glyph_name = font.get_name_char(glyph)
             except KeyError:
                 _log.warning(
                     "No glyph in standard Postscript font {!r} for {!r}"
@@ -864,7 +865,7 @@ def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
         if not found_symbol:
             glyph = '?'
             num = ord(glyph)
-            symbol_name = font.get_name_char(glyph)
+            glyph_name = font.get_name_char(glyph)
 
         offset = 0
 
@@ -890,7 +891,8 @@ def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True):
             fontsize        = fontsize,
             postscript_name = font.get_fontname(),
             metrics         = metrics,
-            symbol_name     = symbol_name,
+            glyph_name      = glyph_name,
+            symbol_name     = glyph_name,  # Backcompat alias.
             num             = num,
             glyph           = glyph,
             offset          = offset
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 9ca791db0c5a..bd0c370f1cba 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -1063,12 +1063,12 @@ def createType1Descriptor(self, t1font, fontfile):
 
         return fontdescObject
 
-    def _get_xobject_symbol_name(self, filename, symbol_name):
+    def _get_xobject_glyph_name(self, filename, glyph_name):
         Fx = self.fontName(filename)
         return "-".join([
             Fx.name.decode(),
             os.path.splitext(os.path.basename(filename))[0],
-            symbol_name])
+            glyph_name])
 
     _identityToUnicodeCMap = b"""/CIDInit /ProcSet findresource begin
 12 dict begin
@@ -1204,7 +1204,7 @@ def get_char_width(charcode):
                 # Send the glyphs with ccode > 255 to the XObject dictionary,
                 # and the others to the font itself
                 if charname in multi_byte_chars:
-                    name = self._get_xobject_symbol_name(filename, charname)
+                    name = self._get_xobject_glyph_name(filename, charname)
                     self.multi_byte_charprocs[name] = charprocObject
                 else:
                     charprocs[charname] = charprocObject
@@ -1347,7 +1347,7 @@ def embedTTFType42(font, characters, descriptor):
                 self.currentstream.write(stream)
                 self.endStream()
 
-                name = self._get_xobject_symbol_name(filename, charname)
+                name = self._get_xobject_glyph_name(filename, charname)
                 self.multi_byte_charprocs[name] = charprocObject
 
             # CIDToGIDMap stream
@@ -2417,8 +2417,8 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
 
     def _draw_xobject_glyph(self, font, fontsize, glyph_idx, x, y):
         """Draw a multibyte character from a Type 3 font as an XObject."""
-        symbol_name = font.get_glyph_name(glyph_idx)
-        name = self.file._get_xobject_symbol_name(font.fname, symbol_name)
+        glyph_name = font.get_glyph_name(glyph_idx)
+        name = self.file._get_xobject_glyph_name(font.fname, glyph_name)
         self.file.output(
             Op.gsave,
             0.001 * fontsize, 0, 0, 0.001 * fontsize, x, y, Op.concat_matrix,
diff --git a/lib/matplotlib/backends/backend_ps.py b/lib/matplotlib/backends/backend_ps.py
index 93d0705ae363..c44f89c638d9 100644
--- a/lib/matplotlib/backends/backend_ps.py
+++ b/lib/matplotlib/backends/backend_ps.py
@@ -701,12 +701,12 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
                 lastfont = font.postscript_name, fontsize
                 self._pswriter.write(
                     f"/{font.postscript_name} {fontsize} selectfont\n")
-            symbol_name = (
+            glyph_name = (
                 font.get_name_char(chr(num)) if isinstance(font, AFM) else
                 font.get_glyph_name(font.get_char_index(num)))
             self._pswriter.write(
                 f"{ox:f} {oy:f} moveto\n"
-                f"/{symbol_name} glyphshow\n")
+                f"/{glyph_name} glyphshow\n")
         for ox, oy, w, h in rects:
             self._pswriter.write(f"{ox} {oy} {w} {h} rectfill\n")
         self._pswriter.write("grestore\n")