PHP code in menu links
I finally figured this out.
YES it is possible to have dynamic menus in Drupal.

You start by enabling dynamic access to menu item with the ['alter'] flag and hook_menu_link_alter(&amp;$item).

function mycode_menu_link_alter(&amp;$item) {
    if($item['menu_name'] == 'user-menu'){
        $item['options']['alter'] = TRUE;
    }
}


Note that menu_link_alter works on a menu item (not the whole menu) and needs to be trigered by editing and saving that item (for example disable->save->enable->save->).

Once the menu item is activated, I can use
hook_translated_menu_link_alter(&amp;$item, $map)

function mycode_translated_menu_link_alter(&amp;$item, $map){
    //drupal_set_message("Menu: ".$item['menu_name']." Item: ".$item['title']
    if($item['menu_name'] == 'user-menu'){
        global $user;
        $item['title'] = "Hi: $user-&gt;name";
    }
}


Other very useful thing you can do is to disable the menu link

$item['hidden'] = TRUE;


or (my favorite) change the links

[...];    
if($item['menu_name'] == 'main-menu'){
   switch ($item['title']){
       case "Home":
            $item['href'] = 'not/home/page';
[...]