diff --git a/asyncpg/connection.py b/asyncpg/connection.py
index 365ab416..73cb6e66 100644
--- a/asyncpg/connection.py
+++ b/asyncpg/connection.py
@@ -1416,6 +1416,7 @@ def _mark_stmts_as_closed(self):
     def _maybe_gc_stmt(self, stmt):
         if (
             stmt.refs == 0
+            and stmt.name
             and not self._stmt_cache.has(
                 (stmt.query, stmt.record_class, stmt.ignore_custom_codec)
             )