I don’t think money has any effect on it. Some billionaires are willing to keep to themselves and roll in their money pit. Some billionaires try to buy the white house and publish a book with their face on it. If they don’t care what people think, they’re wasting a lot of money on something they don’t care about.
Also in Japan, if someone refers to themself with their own name, that’s seen as childish or arrogant.
If your first person pronoun is the same as someone referring to you in third person, then you are referring to yourself in third person every time you refer to yourself in first person. And since the idea of a first person neopronoun is exceedingly rare, most people will only think of you as speaking in the third person.