I would not feel comfortable with someone else answering my T's phone at our scheduled time. I've never been to a therapist who uses an answering service; that seems like a rather outdated practice for a therapist in private practice. I've been to medical doctors who use an after hours answering service, and the service always identifies themselves: "Hello, this is the after hours service. Is this an emergency?" I can't imagine that a T would have a service answer for her when she knows she is expecting a client to call in for an appointment. It sounds much more likely that this is someone who lives in T's house (like a partner). I would NOT feel at all comfortable with T's family member/partner answering the phone. It would give that person access to my phone number, my name, etc. I expect that information to be confidential.