Over here if you're NHS ( I guess it's different if you go private) it's pretty standard to see any number of other people in the waiting rooms due to local metal health teams (pdocs, cpn's, T's, social workers etc) all working out of the same building.
I just keep my eyes on the floor, and try to figure out a little bit about these other people by just looking at their shoes.

When I was 18/19 I did walk out of the office and saw the Mum of a kid I used to look after. I knew exactly why she was there, but it was massively awkward for me as my mental health was, and still is, something i keep very private.