I agree with your answer, but not that your question is the question. Some that I think are closer:

Does an artist own their name? Yes. I can’t publish a work of art and say “authored by savant_penguin”.

Can I sell art with product name “in the style of savant_penguin”? I think this varies by jurisdiction; it’s not going to be legal in the EU I think. It might well be in the US.

Edit: fleshed out more thoroughly by someone else already: https://news.ycombinator.com/item?id=33423857