Changing the license plate is fine I think. They're called vanity plates for a reason, and if the government body that issues them decides it's no good then that's that. If his last name was Fuccboi or if we were talking the name of his WoW character this would probably end the same way.
No he shouldn't have to change his name or the private company. Things like license plates that support more shortform and slang modalities of language where it would be more easily misunderstood, I think disallowing it is unfortunate but understandable.
Georgia looks like. Florida?
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"This will be a fight against overwhelming odds from which survival cannot be expected. We will do what damage we can."
-- Capt. Copeland
This is pretty funny... vanity plates aren't something to get your panties in a bunch over. He shouldn't be ashamed of his last name... but it can be viewed as offensive on the back of a car with out context, end of story.