"Are you saying you don't have a core personality?"
Not when I'm around other people, no, I'm always in a different 'role' when I'm talking to people, heck I don't know what being myself around someone feels like, I don't think I have a 'self'.
I have many personas for many situations. It seldom has to do with the people I'm around so much so, but I do like to keep it mostly consistent around them. I don't have a strong "self" in the same sense that most people call it that. It's more just a sense that I'm someone, and I have likes, dislikes, etc...
I also create and destroy new personas depending on which ones work better than others. Currently, I've noticed that pretending to care and pretending to be average works to blend in. Though I try to balance things out, so as to not appear too normal either.
People tend to see me as caring and empathetic, these things I routinely have faked since my late teens at least. Alongside feigning humility and other things to make me seem less arrogant and distant. I don't fake emotions as much as I used to, as I've become less dependant on others for my own sustainance, now I need people less.