diff --git a/pkg/ddl/column.go b/pkg/ddl/column.go
index ee2e1304ebae5..f575aaf255e91 100644
--- a/pkg/ddl/column.go
+++ b/pkg/ddl/column.go
@@ -1304,8 +1304,8 @@ func getChangingColumnOriginName(changingColumn *model.ColumnInfo) string {
 	return columnName[:pos]
 }
 
-func getExpressionIndexOriginName(expressionIdx *model.ColumnInfo) string {
-	columnName := strings.TrimPrefix(expressionIdx.Name.O, expressionIndexPrefix+"_")
+func getExpressionIndexOriginName(originalName pmodel.CIStr) string {
+	columnName := strings.TrimPrefix(originalName.O, expressionIndexPrefix+"_")
 	var pos int
 	if pos = strings.LastIndex(columnName, "_"); pos == -1 {
 		return columnName
diff --git a/pkg/ddl/db_integration_test.go b/pkg/ddl/db_integration_test.go
index ae397fc44ea9d..1d8821f4a3bf8 100644
--- a/pkg/ddl/db_integration_test.go
+++ b/pkg/ddl/db_integration_test.go
@@ -1333,7 +1333,8 @@ func assertAlterWarnExec(tk *testkit.TestKit, t *testing.T, sql string) {
 }
 
 func TestAlterAlgorithm(t *testing.T) {
-	store := testkit.CreateMockStore(t, mockstore.WithDDLChecker())
+	store, dom := testkit.CreateMockStoreAndDomain(t, mockstore.WithDDLChecker())
+	ddlChecker := dom.DDL().(*schematracker.Checker)
 
 	tk := testkit.NewTestKit(t, store)
 	tk.MustExec("use test")
@@ -1376,6 +1377,20 @@ func TestAlterAlgorithm(t *testing.T) {
 	tk.MustExec("alter table t rename index idx_c2 to idx_c, ALGORITHM=INSTANT")
 	tk.MustExec("alter table t rename index idx_c to idx_c1, ALGORITHM=DEFAULT")
 
+	// Test corner case for renameIndexes
+	tk.MustExec(`create table tscalar(c1 int, col_1_1 int, key col_1(col_1_1))`)
+	tk.MustExec("alter table tscalar rename index col_1 to col_2")
+	tk.MustExec("admin check table tscalar")
+	tk.MustExec("drop table tscalar")
+
+	// Test rename index with scalar function
+	ddlChecker.Disable()
+	tk.MustExec(`create table tscalar(id int, col_1 json, KEY idx_1 ((cast(col_1 as char(64) array))))`)
+	tk.MustExec("alter table tscalar rename index idx_1 to idx_1_1")
+	tk.MustExec("admin check table tscalar")
+	tk.MustExec("drop table tscalar")
+	ddlChecker.Enable()
+
 	// partition.
 	assertAlterWarnExec(tk, t, "alter table t ALGORITHM=COPY, truncate partition p1")
 	assertAlterWarnExec(tk, t, "alter table t ALGORITHM=INPLACE, truncate partition p2")
diff --git a/pkg/ddl/index.go b/pkg/ddl/index.go
index 897f788c26542..2f292703bff7d 100644
--- a/pkg/ddl/index.go
+++ b/pkg/ddl/index.go
@@ -2611,12 +2611,19 @@ func renameIndexes(tblInfo *model.TableInfo, from, to pmodel.CIStr) {
 			idx.Name.L = strings.Replace(idx.Name.L, from.L, to.L, 1)
 			idx.Name.O = strings.Replace(idx.Name.O, from.O, to.O, 1)
 		}
+		for _, col := range idx.Columns {
+			originalCol := tblInfo.Columns[col.Offset]
+			if originalCol.Hidden && getExpressionIndexOriginName(col.Name) == from.O {
+				col.Name.L = strings.Replace(col.Name.L, from.L, to.L, 1)
+				col.Name.O = strings.Replace(col.Name.O, from.O, to.O, 1)
+			}
+		}
 	}
 }
 
 func renameHiddenColumns(tblInfo *model.TableInfo, from, to pmodel.CIStr) {
 	for _, col := range tblInfo.Columns {
-		if col.Hidden && getExpressionIndexOriginName(col) == from.O {
+		if col.Hidden && getExpressionIndexOriginName(col.Name) == from.O {
 			col.Name.L = strings.Replace(col.Name.L, from.L, to.L, 1)
 			col.Name.O = strings.Replace(col.Name.O, from.O, to.O, 1)
 		}
diff --git a/pkg/ddl/schematracker/BUILD.bazel b/pkg/ddl/schematracker/BUILD.bazel
index de05d2d58abcb..209b1af2b649e 100644
--- a/pkg/ddl/schematracker/BUILD.bazel
+++ b/pkg/ddl/schematracker/BUILD.bazel
@@ -47,7 +47,7 @@ go_test(
     ],
     embed = [":schematracker"],
     flaky = True,
-    shard_count = 15,
+    shard_count = 16,
     deps = [
         "//pkg/executor",
         "//pkg/infoschema",
diff --git a/pkg/ddl/schematracker/checker.go b/pkg/ddl/schematracker/checker.go
index 4742209f46799..e2d09a1027e55 100644
--- a/pkg/ddl/schematracker/checker.go
+++ b/pkg/ddl/schematracker/checker.go
@@ -223,7 +223,7 @@ func (*Checker) RecoverSchema(_ sessionctx.Context, _ *ddl.RecoverSchemaInfo) (e
 // CreateTable implements the DDL interface.
 func (d *Checker) CreateTable(ctx sessionctx.Context, stmt *ast.CreateTableStmt) error {
 	err := d.realExecutor.CreateTable(ctx, stmt)
-	if err != nil {
+	if err != nil || d.closed.Load() {
 		return err
 	}
 
@@ -332,7 +332,7 @@ func (d *Checker) DropIndex(ctx sessionctx.Context, stmt *ast.DropIndexStmt) err
 // AlterTable implements the DDL interface.
 func (d *Checker) AlterTable(ctx context.Context, sctx sessionctx.Context, stmt *ast.AlterTableStmt) error {
 	err := d.realExecutor.AlterTable(ctx, sctx, stmt)
-	if err != nil {
+	if err != nil || d.closed.Load() {
 		return err
 	}
 
diff --git a/pkg/ddl/schematracker/dm_tracker_test.go b/pkg/ddl/schematracker/dm_tracker_test.go
index 89b47bc8b21a5..9ab0e28f90a67 100644
--- a/pkg/ddl/schematracker/dm_tracker_test.go
+++ b/pkg/ddl/schematracker/dm_tracker_test.go
@@ -219,6 +219,24 @@ func TestIndexLength(t *testing.T) {
 	checkShowCreateTable(t, tblInfo, expected)
 }
 
+func TestCreateTableWithIndex(t *testing.T) {
+	// See issue 56045
+	sql := "create table test.t(col_1 json, KEY idx_1 ((cast(col_1 as char(64) array))))"
+	tracker := schematracker.NewSchemaTracker(2)
+	tracker.CreateTestDB(nil)
+	execCreate(t, tracker, sql)
+
+	sql = "alter table test.t rename index idx_1 to idx_1_1"
+	execAlter(t, tracker, sql)
+
+	tblInfo := mustTableByName(t, tracker, "test", "t")
+	expected := "CREATE TABLE `t` (\n" +
+		"  `col_1` json DEFAULT NULL,\n" +
+		"  KEY `idx_1_1` ((cast(`col_1` as char(64) array)))\n" +
+		") ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_bin"
+	checkShowCreateTable(t, tblInfo, expected)
+}
+
 func TestIssue5092(t *testing.T) {
 	// copy TestIssue5092 in db_integration_test.go
 	sql := "create table test.t (a int)"