My therapist and doctor could find me if they wanted to. The office has my phone number and address on fjke and I talk about where I work and go to grad school. That info I don't think they keep in my file, so they may only know because I bring it up in session.

Because of confidentiality your T cannot try to find you at work without your direct instruction to do so. My Ts office requires I give them permission to leave voicemails at my home phone for the same reason. So if you're worried about someone finding out and leaking it to the community you and your father are in, that won't happen (or it shouldn't anyway). If it did, your T would get in trouble; you could even sue in some cases.