No, he can't: using a false address would be fraud against the state and a violation of the laws pertaining to ID; it would be a fraud against anyone who does business with him in reliance on his ID or after viewing/checking it; and it would be grounds for you to sue him for ANY losses or costs you incur due to him representing that he lives at your home (e.g if someone sues him and tries to put a lien on your home, believing it is his).You can contact not just the DMV but also your local police and the state attorney general's office about this: what he is doing is a crime, and can and probably should get law enforcement involved. If you don't want to do that immediately, you can give him a week or two to correct this, then go to the authorities.