[2.7] bpo-31107: Fix copyreg mangled slot names calculation. (GH-2989). (#3004)

(cherry picked from commit c4c9866064f03646c686d7e08b00aeb203c35c19)
diff --git a/Lib/copy_reg.py b/Lib/copy_reg.py
index db17150..8943077 100644
--- a/Lib/copy_reg.py
+++ b/Lib/copy_reg.py
@@ -127,7 +127,11 @@
                         continue
                     # mangled names
                     elif name.startswith('__') and not name.endswith('__'):
-                        names.append('_%s%s' % (c.__name__, name))
+                        stripped = c.__name__.lstrip('_')
+                        if stripped:
+                            names.append('_%s%s' % (stripped, name))
+                        else:
+                            names.append(name)
                     else:
                         names.append(name)
 
diff --git a/Lib/test/test_copy_reg.py b/Lib/test/test_copy_reg.py
index 8cdb8b7..17ccbd0 100644
--- a/Lib/test/test_copy_reg.py
+++ b/Lib/test/test_copy_reg.py
@@ -17,6 +17,12 @@
 class WithPrivate(object):
     __slots__ = ('__spam',)
 
+class _WithLeadingUnderscoreAndPrivate(object):
+    __slots__ = ('__spam',)
+
+class ___(object):
+    __slots__ = ('__spam',)
+
 class WithSingleString(object):
     __slots__ = 'spam'
 
@@ -105,6 +111,10 @@
         self.assertEqual(copy_reg._slotnames(WithWeakref), [])
         expected = ['_WithPrivate__spam']
         self.assertEqual(copy_reg._slotnames(WithPrivate), expected)
+        expected = ['_WithLeadingUnderscoreAndPrivate__spam']
+        self.assertEqual(copy_reg._slotnames(_WithLeadingUnderscoreAndPrivate),
+                         expected)
+        self.assertEqual(copy_reg._slotnames(___), ['__spam'])
         self.assertEqual(copy_reg._slotnames(WithSingleString), ['spam'])
         expected = ['eggs', 'spam']
         expected.sort()