You can create two different menu items with different name and different AccessLevel:
'My XXX' -> Guest Access Level
'Mijn XXX - log out' -> Registered Access Level

with this the Guest user will see 'My XXX' and registered will see 'Mijn XXX - log out'

Thanks, This was logical thinking.

BTW On this site you can log out directly in the submenu of 'Account', on the right-top. In my submenu I also built in a logout menu-item, but that is a (menu)link to the logout button in the component-area. You must click again. How can I get it just like you, thats much nicer for the user.

groet,
Lianne

We have do this with Joomla core hack, But I think that there are some plugin to do this.

Anyway our solution:
- Create a menu item of type System->External URL and put in URL parameter this:

index.php?option=com_users&task=user.logout

- Now to work and not give errors, you must comment the line 89 of file /components/com_users/controllers/user.php.

//JSession::checkToken('request') or jexit(JText::_('JInvalid_Token'));