how to display only the domain name (up to LTD)

There aren't any built-in options for doing this in link.module. You'll need to theme your output in a .tpl.php file such as node-link.tpl.php (if "link" is the name of your content type). You could also achieve the same thing by using contemplate module.

Closing after 2 weeks with no activity.

This can help:
http://php.net/manual/en/function.parse-url.php
#472766: Display Domain Name Only