The way it mostly works is that if a company hires a Morgan Freeman impersonator to do the voice over for their car commercial, Morgan Freeman can sue them for using his likeness without permission:

https://law.justia.com/cases/federal/appellate-courts/F2/849...

> We need not and do not go so far as to hold that every imitation of a voice to advertise merchandise is actionable. We hold only that when a distinctive voice of a professional singer is widely known and is deliberately imitated in order to sell a product, the sellers have appropriated what is not theirs and have committed a tort in California.