what is genji's full name?

Hikaru Genji, 光源氏. Hikaru means: light. The surnames of the aristocrates could be read in two ways: you could use on-yomi, the Chinese reading, then it`s: Genji, or you could use the japanese reading, kun-yomi, and read it: Minamoto.

Genji was given the appellation Hikaru no Kimi, 光の君 in his youth. He is also referred to in the book as Rokujō no In, 六条院 sometimes abbreviated as In, 院. His given name is never referred to in the course of the story.