T calls me by my first name and I call her by her first name by her request.

I wouldn't care if she wanted me to call her differently.
I don't use her name much unless on the phone calling for scheduling. In person not so much.

But I would intensely object being called by my last name. I am a teacher. I am called Ms. "So and so" all day long. I don't want to be called by my last name outside of work

I seriously would feel annoyed up to the point of switching therapists.

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