I have no problems with people, even therapists, looking anyone up and finding information that is publicly available. I also have no problem if anyone, clients or therapists, want to decide who they will and will not work with and as long as the rules on each side are clear, if one party or the other violates that agreement, I have no problem with the therapist quitting or the client quitting. I have had students who tried looking me up (I do not participate in facebook etc and have very little non-professional info on the web). I have had students drive past my house and that did not bother me.
But legally speaking, it is not stalking without more. And what constitutes stalking varies a lot state to state in the u.s.

(I take great issue with a therapist believing they get to fire a client. The client is the one who hires the therapist. The therapist may quit, but not fire.)