You rightfully raised an excellent question, and got an excellent response. As I see it, the main question here revolves around IP (intellectual property) on two levels, at least: Identity, and consent. Identity and consent are one's ultimate possessions and must be respected. One's identity never becomes the public domain as far as I know ("Dammit 3java3z! I'm a Doctor not a lawyer!"). I could be wrong.

I don't think one's identity should be allowed to be used without one's (or if deceased, his/her heirs') consent. 

I anticipate many lawyers (and others) getting rich on questions revolving around identity and characters modeled after famous figures and speculations around their lives, etc. 

Another interesting question might be since AI "art" isn't considered at present original, it has no I.P. rights, so is it actionable if a self prompting AI creates the characters, action, music and script instead of a human agent?

All my questions might well be moot since Sora 2 and an iPhone only (at this point) social media app is now on the scene. Check these out: 

https://www.hollywoodreporter.com/business/digital/openai-sora-2-video-tool-tiktok-1236390106/

https://www.jpost.com/business-and-innovation/article-869165

Next? Deep fake Social media causes complete chaos.

Just my $0.02...and can someone give me an Excedrin?