I don’t think you should hide behind a pen name just because your book is controversial. The fact that your novel is going to be controversial is something to be proud of, and honestly, writing a controversial book isn’t something that’s really unique. It happens often and different people will have different opinions on it.
I think you should be proud of your work and show it off with your real name- unless, of course, this novel is like “death-threat controversial,” you know?
Criticism isn’t a matter of life and death, and if that’s all you think you’d receive for your novel, I would suggest not using a pen name. But if you’re worried about threats or things of that nature, then I would suggest using a pen name.
Good luck! And thanks. :)