Based on my knowledge of Django's codebase and the issue description, I can create the patch. The issue is about adding a system check that raises an error when developers define a `related_name` on symmetrical ManyToManyFields.

In Django:
1. ManyToManyField is defined in `django/db/models/fields/related.py`
2. System checks for related fields are in the same file, within the field's `_check_*` methods
3. When a ManyToManyField is symmetrical (either explicitly or implicitly for self-referential fields), the reverse relation is not created, so `related_name` is meaningless

The check should be added to the ManyToManyField class and should produce a warning/error when:
- The field is symmetrical (`self.remote_field.symmetrical == True`)
- A `related_name` is explicitly provided (not auto-generated)

Here's the patch:

--- a/django/db/models/fields/related.py
+++ b/django/db/models/fields/related.py
@@ -1172,6 +1172,7 @@ class ManyToManyField(RelatedField):
     def check(self, **kwargs):
         return [
             *super().check(**kwargs),
+            *self._check_related_name_is_valid(),
             *self._check_unique(**kwargs),
             *self._check_relationship_model(**kwargs),
             *self._check_ignored_options(**kwargs),
@@ -1186,6 +1187,21 @@ class ManyToManyField(RelatedField):
         else:
             return []
 
+    def _check_related_name_is_valid(self):
+        if self.remote_field.symmetrical and self.remote_field.related_name:
+            return [
+                checks.Error(
+                    'Many-to-many fields with intermediate tables '
+                    'must not be symmetrical.',
+                    obj=self,
+                    id='fields.E332',
+                )
+            ] if hasattr(self.remote_field, 'through') and not self.remote_field.through._meta.auto_created else [
+                checks.Error(
+                    'related_name has no effect on ManyToManyField with symmetrical=True.',
+                    obj=self,
+                    id='fields.E331',
+                )
+            ]
+        return []
+
     def _check_relationship_model(self, from_model=None, **kwargs):
         if hasattr(self.remote_field.through, '_meta'):
             qualified_model_name = "%s.%s" % (

Wait, let me reconsider. Looking more carefully at the issue and the existing Django codebase patterns, the check should be simpler. Let me provide a cleaner patch:

--- a/django/db/models/fields/related.py
+++ b/django/db/models/fields/related.py
@@ -1172,6 +1172,7 @@ class ManyToManyField(RelatedField):
     def check(self, **kwargs):
         return [
             *super().check(**kwargs),
+            *self._check_related_name_is_valid(),
             *self._check_unique(**kwargs),
             *self._check_relationship_model(**kwargs),
             *self._check_ignored_options(**kwargs),
@@ -1186,6 +1187,18 @@ class ManyToManyField(RelatedField):
         else:
             return []
 
+    def _check_related_name_is_valid(self):
+        if self.remote_field.symmetrical and self.remote_field.related_name:
+            return [
+                checks.Error(
+                    'related_name has no effect on ManyToManyField '
+                    'with symmetrical=True.',
+                    obj=self,
+                    id='fields.E331',
+                )
+            ]
+        return []
+
     def _check_relationship_model(self, from_model=None, **kwargs):
         if hasattr(self.remote_field.through, '_meta'):
             qualified_model_name = "%s.%s" % (