"Well crap now I'm a public figure because of this, I don't really have a choice if I want to do my job well in the future."
Using "forced" may be a little clumsy, but it's certainly directionally correct.
If he doesn't think he can do psychotherapy very while while he's a "public figure" (his name being in the paper a single time), why is he opening up his own practice?
I have already posted his own quotes in this comment chain, where he admits his case is weak and that anonymity is merely his preference.
He is opening his practice only to patients that are comfortable with him and he is comfortable with. That's a different situation than working with who the hospital assigns him. Also he does say they were 'tentatively' willing to still keep him but it sounds like there was friction nonetheless.