Should at least the heroes of Socratic have their full name listed on their profile?
I would say not really.
Socratic Heroes are not part of the Socratic team per se, we are members of the community just like any other contributor or student - think of us as part of the extended Socratic family.
You can find the personal info of the actual Socratic team members here
We, i.e. the Heroes, are regular contributors who try to give a helping hand around the community in whichever way we can: help new contributors get accustomed to the community, provide instructions about answer formatting, answer structure, keep the site abuse and spam free, things of that nature.
Moderator stuff, basically.
This being said, I do not think that giving our full names would have an impact on our activities on the site.
We are volunteers who contribute and moderate site content in our spare time, which is why we can have nicknames and weird profile photos ( I speak for myself here :P).
Now, I assume that you have a specific reason for asking this, maybe? Do you think that using our full names would have a different impact on the community?