diff --git a/sqlglot-integration-tests b/sqlglot-integration-tests
index f0c1c9b057..21043c686d 160000
--- a/sqlglot-integration-tests
+++ b/sqlglot-integration-tests
@@ -1 +1 @@
-Subproject commit f0c1c9b0578e83d7005e21f4862eafde4d6fb282
+Subproject commit 21043c686d54bfc8eee51280c8118f22f5cf1923
diff --git a/sqlglot/optimizer/canonicalize_internal_names.py b/sqlglot/optimizer/canonicalize_internal_names.py
index 7004e29712..15865f55d9 100644
--- a/sqlglot/optimizer/canonicalize_internal_names.py
+++ b/sqlglot/optimizer/canonicalize_internal_names.py
@@ -255,10 +255,11 @@ def _canon(ident: exp.Identifier, name: str) -> None:
 
         scope_outputs[id(scope_expr)] = output_map
 
-        # Unqualified alias references (ORDER BY a, HAVING a > 5, ...)
+        # Unqualified alias references (ORDER BY a, HAVING a > 5, ...).
         for col in find_all_in_scope(scope_expr, exp.Column):
-            if not col.table and col.name in output_map:
-                _canon(col.this, output_map[col.name])
+            # Only rewrite when the alias is actually being renamed
+            if not col.table and (canon := output_map.get(col.name)) and canon != col.name:
+                _canon(col.this, canon)
 
         # UBN matches branches by original alias. When both branches are internal
         # and aliased to distinct _cN, matching originals land on different slots