Hmmmm.......With him being a public figure, maybe he has no say anyway?
Well, I dont know about the legal aspects of this. However, know how the President is EXTREMELY keen on licensing his name to other companies around the world. I suspect he demanded an "escape" clause in the contract that allows him to back out if he changes his mind at ANY time.
Control over name and image is for when he was a private citizen. Once he chose to run for office and even more so with becoming president, all bets are off. Unless the portrayal of him is intentionally and seriously false*, anyone can make 'puppets' of any president and have them say and do almost anything.
Disney can have a Trump AA and have a vocal imitator give a speech he never gave nor approved of... if it's not intentional falsehood.*
*Making your 'puppet' say untrue things is allowed if it is satire or parody.