[soult]

You should have asked yourself that question before you registered at Godaddy. If you do not want your name to be associated with your domain, you are now locked in forever. To be honest, I don't even know if other registrars do it any different. (I only know that Nearlyfreespeech.net does not lock you in that way, but not about others like namecheap.)

Gandi.net does not offer full whois privacy by the way, so your name will always be revealed.

[elliottcarlson]

Note though that it is just your name and not other associated information.