Some registrars off an option that does just that--for an additional fee. I don't think DH offers it on their domains, though. (Edit: I just wanted to make it clear that I meant DH as a registrar--not a host. You can host domains here regardless of where they're registered, with or without privacy protection.)
I know Namecheap throws it in for free the first year. Godaddy offers DomainsByProxy, Yahoo has something similar, etc...
Just don't enter fraudulent info as an alternative, incase you ever need to prove the domain is really yours. For semi-privacy, go with a small/cheap PO box and use that as your address.
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