Public info is public info so obviously it's fair game. But I agree with stopdog that I don't think therapists are all that interested in clients to begin with. Problem is, some clients want to ascribe a super deep meaning to the therapist looking them up/thinking about them. Honestly I doubt it's super meaningful. Not in the way a lot of clients wish to matter to their therapists. I also have googled some of my clients (I work in marketing) and sometimes they randomly pop into my mind. Doesn't mean much other than my brain randomly selects information.