My T is also a PsyD and yes, I do address her by her first name (that's how she introduced herself). It mostly happens only when we correspond out of session - sometimes by text message, and if I leave a voicemail. I also refer to her by her first name when talking about her to my pdoc.

It is important to me that my T introduces themselves by first name. I would struggle with the intimacy of the relationship juxtaposed with calling them "Dr. so-and-so".

I was thrilled when my pdoc introduced herself by her first name. She does longer appointments (25 minutes or so), with some therapy as well as med management. Although her office staff always reference her as Dr, I do not.

As far as I am concerned, my T and pdoc are just people. They are no better than me, we are equals. They have more education in medicine and psychology but I have more education in science, mathematics and engineering (no, I do not have a PhD).