I agree with both those points. Ingomar, I would just ask myself do I really want to continue with a counselor who has done these objectionable things so early in the relationship? If you don't return to see her again, you really haven't lost much time or effort or energy. There are lots of therapists out there. Get one who will not dance on the edge of client confidentiality rights and not force/manipulate you to reveal things you don't want to.
Rapunzel, I believe that the therapist did violate confidentiality to her original client (the male). She revealed his name in therapy with another client. A therapist should never reveal the names of clients to each other unless he has both of their permission. If they give this information up voluntarily (no tricks, no badgering), then that is different. If I were the second (female) client, I would be very concerned at this violation of her male client's confidentiality and wonder if she would also violate my confidentiality so casually at some point in the future.
I just had a first session with a new therapist yesterday. The very first thing he discussed was confidentiality. He made sure we both understood the protection I was guaranteed, and this brief discussion gave me confidence in him and his practice. Confidentiality is so important.