They shouldn’t be allowed to misuse his name by claiming he supports them and their efforts in ways that he doesn’t, but the name of the recently past president could well be fodder for use in fundraising on either side in ways that he shouldn’t be able to stop.
My thought is the law doesn’t give him much in the way of “legal rights” in this area, and that it won’t be a judge deciding where the dust settles - meaning the threat to sue is hollow.
This is a public distancing, whether or not the party apparatchiks respect Trump’s stated wishes.