diff --git a/packages/edit-post/src/components/header/template-title/edit-template-title.js b/packages/edit-post/src/components/header/template-title/edit-template-title.js
index 2865e674b341fd..8f2ccf8ef56fbb 100644
--- a/packages/edit-post/src/components/header/template-title/edit-template-title.js
+++ b/packages/edit-post/src/components/header/template-title/edit-template-title.js
@@ -29,7 +29,8 @@ export default function EditTemplateTitle() {
 	const { getEditorSettings } = useSelect( editorStore );
 	const { updateEditorSettings } = useDispatch( editorStore );
 
-	if ( template.has_theme_file ) {
+	// Only user-created and non-default templates can change the name.
+	if ( ! template.is_custom || template.has_theme_file ) {
 		return null;
 	}
 
diff --git a/packages/edit-site/src/components/template-details/index.js b/packages/edit-site/src/components/template-details/index.js
index 5963040b7ef5bd..71bbb41be2860c 100644
--- a/packages/edit-site/src/components/template-details/index.js
+++ b/packages/edit-site/src/components/template-details/index.js
@@ -50,6 +50,9 @@ export default function TemplateDetails( { template, onClose } ) {
 		postId: undefined,
 	} );
 
+	// Only user-created and non-default templates can change the name.
+	const canEditTitle = template.is_custom && ! template.has_theme_file;
+
 	if ( ! template ) {
 		return null;
 	}
@@ -62,7 +65,7 @@ export default function TemplateDetails( { template, onClose } ) {
 	return (
 		<div className="edit-site-template-details">
 			<div className="edit-site-template-details__group">
-				{ template.is_custom ? (
+				{ canEditTitle ? (
 					<EditTemplateTitle template={ template } />
 				) : (
 					<Heading