Function

function give_profile_name($atts){
    $user=wp_get_current_user();
    $name=$user->user_firstname;
    return $name;
}

add_shortcode('profile_name', 'give_profile_name');

add_filter( 'wp_nav_menu_objects', 'my_dynamic_menu_items' );
function my_dynamic_menu_items( $menu_items ) {
    foreach ( $menu_items as $menu_item ) {
        if ( strpos($menu_item->title, '#profile_name#') !== false) {
                $menu_item->title =  str_replace("#profile_name#",  wp_get_current_user()->billing_company, $menu_item->title);
        }
    }

    return $menu_items;

<!-- no campo "billing_company" você muda pra "display_name"... ou outra coisa
https://codex.wordpress.org/Function_Reference/wp_get_current_user

no menu você coloca "#profile_name#" sem aspas... -->