C.C is just an alias for her character, her true name is never revealed in the series.

C.C is the one to give Lelouch the Geass, she is currently a possessor of the Code. The Code is activated when the Geass user takes the life of another Geass user who has reached immortality.

C.C's original Geass ability was the ability to charm others. She grew up as a slave and had a very shy personality, contrary to her current one.

C.C's main goal was to die and escape her life of immortality. However, Lelouch refused to let her die a sad death and vowed to never let her feel lonely again.

Throughout the story, Lelouch is represented as the "King" and C.C is represented as his "Queen". The two share a deep relationship and trust each other as they call each other accomplices.

All in all, C.C is an awesome character and I totally ship her with Lelouch! :D