I've seen it asserted a lot, but I'm not clear on the exact mechanism in play here.

Is it copyright?

Is it some protected legal mechanism encoded in law, or is it agreement(s) between parties (Broadcasters/TV/Film producers)?

Is it only in play if you explicitly say it's a particular person? Can you use an impersonator to voice over something without referencing the person in question/give no grounds to suggest it's a particular person? What if you hire a good lookalike? A soundalike?