Vanity license plate

I'd like to get a vanity license plate but I have a question regarding registration.

The registration just renewed a couple of months ago, with the current (non-vanity) plate info on it. If I get a new plate, would I have to pay again to reregister the vehicle? Or would an updated copy with the vanity plate info be sent?

Any other info I should know?

I checked the DMV website but can't find what I'm looking for. Thanks!