What is C2's actual name?
Answered here.

It is unknown by design. C2's name is obscured when she tells it to Lelouch in the cave (first sesason, episode 5 to 8 -ish).

Nowhere it is written, and given the producers inclination to secrecy, it won't be revealed.

It is speculated that the name begins with the letter C, but that is all.