We can see ghost images of both of Skinny Dippin's prior names on the transom... and we don't really care. The dinghy covers them and we moved the name up to the sundeck surround. See Bess' avatar. Pretty sure it will ghost-in too, but up there will be easy to paint over if, in the future, there are new owners.
I have a quick question: If we ever sell her, can we, in a sales contract, require or request that the new owners to change the name?
Tom-
You can request anything. That doesn't mean it will happen though. "Require" ? And how would you enforce it?
Unless you find a way to copyright or trademark your boat's name there's nothing you can do to keep other people from using the same name as yours.
There are currently 39 "HIGH COTTON"s documented plus a few more variations of the name.
You could, of course, rename it before you sell it. Name it something like "Reel Knotty" and the next owner is sure to rename it.