When I say "who you are", I mean could your T find you if he/she wanted to? Basically it's the question of anonymity...

This was a little touchy for me because my father is a local businessman (I travel ~15 miles to a small city for my sessions). I work for him and during the first session I told my T where I work and just once referred to him as "my boss". She then asked "How do you get along with your boss?". This was the moment I knew I had to tell her and I did.

I was wondering if I should have told her the name of the company, but then again she knows my name and could have googled it easily.

I am just curious if you were paranoid about this.