When I turned forty, I decided to not refer to people by their titles anymore (Dr., Mr., Mrs., Ms., Professor, Father, etc.). I was an adult and we could all be on a first name basis. I have followed this decision. I encourage my clients to call me Natalie, not Dr. Gelman. I respect whatever choice they make.
Last night I went to a small social gathering to interact with the new Rabbi of the Temple I belong to. A woman asked her what her first name was. She replied, “Rabbi.” She clarified that she would not share her first name because she wants to be called Rabbi in any setting that has to do with her professional role.
I respect her decision. I will not be close to her.