Problem login/register nav menu

I add this code to functions.php for make a login/register in nav menu. But The problem is that all logged in users appear as the site administrator instead of putting his nick.

add_filter('wp_nav_menu_items', 'add_login_logout_link', 10, 2);
function add_login_logout_link($items, $args) {

        ob_start();
        wp_loginout( $_SERVER['REQUEST_URI'] );
        $loginoutlink = ob_get_contents();
        ob_end_clean();
        $items .= '<li>'. $loginoutlink .'</li>';
    return $items;
}
add_filter('wp_nav_menu_items', 'add_register_link', 10, 2);
function add_register_link($items, $args) {

        ob_start();
        wp_register('');
        $registerlink = ob_get_contents();
        ob_end_clean();
        $items .= '<li>'. $registerlink .'</li>';
    return $items;
}