function change_username($user_id, $new_username) {
    global $wpdb;
    $user_id = intval($user_id);
    $new_username = sanitize_user($new_username);
    $wpdb->query( 
        $wpdb->prepare( 
            "UPDATE {$wpdb->users} SET user_login = %s WHERE ID = %d", 
            $new_username, 
            $user_id 
        ) 
    );
    $wpdb->query( 
        $wpdb->prepare( 
            "UPDATE {$wpdb->users} SET display_name = %s WHERE ID = %d", 
            $new_username, 
            $user_id 
        ) 
    );
}

$user_id = x;
$new_username = 'NewUserName';

change_username($user_id, $new_username);