Thank you for your help. Unfortunately, your code did not work out for me. Maybe because I use Thrive Themes as editor. For me following code embedded in functions.php was the solution:
add_filter(
‘wp_pre_insert_user_data’,
function ( $data ) {
$data[‘display_name’] = isset( $_REQUEST[‘name’] ) ? $_REQUEST[‘name’] : $data[‘display_name’];
return $data;
}
);