Genji is the son of the Emperor and Kiri-Tsubo, the Emperor's beloved mistress. Kiri-Tsubo lacks powerful connections and is often the subject of jealous attacks by others at court, some led by the another of the Emperor's mistresses, Lady Koki-den.
Murasaki-no-ue, Genji's real love and wife.
Murasaki no kimi, but once she becomes Hikaru Genji's wife she is called Murasaki no ue.