When I had jobs in the public, the ONLY difference in how I acted there vs home etc is I was quieter. My social anxiety kicked in and I was more shy.I know my T is very silly/funny with me but has said many times "I'm actually very quiet outside of here with most people." and I never believed it until a weird session where we had to have some guy in the building fixing something while we we were there and the guy was asking him things a few times since no one else was around and he got really shy/quiet and I commented on it and he said 'Yes, I have to be comfortable with someone before I am more chatty' thats exactly how I am... so I think for the most part in my case, I see very much who he is.

Besides... it's totally fine to me that people would be different in different situations. I think everyone does that from time to time. I can tell you, my family sees the most quiet/innocent and chill side of me ever... I am not like that at all but because of how my family is, it's the only acceptable way. My T, my friends, they all see the real fun/silly me.... although I am still mostly quiet, ha!

You are right though generally , but just sharing my story here.