I advise against that, because in my experience, when you have a real name and a pseudonym account, there's a strong temptation to post all your edgy, attention-grabbing content to the alt, and all the boring content to your real name account.

Which is really bad for your main account, actually.

Note that some of the most popular personalities on Twitter - Elon Musk, Balaji Srinivasan - take this "carefully moderate your opinions unless it's a pseudonym" approach and stomp all over it. They are the total opposite of that. I think there's a lesson there, too: to really reach the stratosphere (including fame and wealth), as an unknown person, you probably need to take some risks and post risk-taking content, and associate it with a name+face where people can rally to you.

To be clear, I'm not making the moral argument that pseudonyms are cowardly or a moral failing, so don't use them. I'm making the purely self-interested argument that your content is worth money and you should monetize it under your real name, because it's the best vehicle for that.