What would be this clear distinction if the internet was spammed full of you doing things you would never do? Why should anyone care to find out the real you amongst the fake ones?
But anyways different times + Eminem rapped about copycat rappers and not about someone deepfaking your whole being on the internet.
And in a world where there are deepfakes of every famous person.. People will finally stop trusting everything they see online. With the way things are going at the moment we're going to get to that point with or without legislation. Realistically you just won't be able to ban deep fakes worldwide. People will just assume if they come across a video online that it's fake - as they should be doing already in all honesty
If you made a concerted effort to fool people into thinking it's the real person then it'd be illegal. Especially if you're out to hurt them somehow. In the same vein as libel
And in a world where there are deepfakes of every person, famous or not... People won't be able to trust anything they see anywhere. Welcome to Hell.