I was thinking of a bigger picture...Trump transfers his name out so he can put his residency in say, New Jersey? of course, the only reason he would want to do that is if he was going to name another Floridian as his Veep choice. NOT Desantis, but perhaps one of those congressmen/women who have supported him perhaps?
Congratulations for basically being the first poster to ponder the actual implications, and not get stuck on the title. I had some similar thoughts at first, before being amazed at how no one wanted to talk about anything but the superficial title. I didn't dare want to float the possibility of DeSantis becoming VP, though, else some small heads might explode.
I transferred my property to my son many years ago, but kept a Life Estate. Perhaps Trump did the same.