"Luna" can mean "Moon" in a few languages. Also, in ancient Roman religion and myth, Luna is the divine embodiment of the Moon. In the manga, when Luna first met Shark, she introduces herself as "a messenger from the moon". Her Moon-style Deck, D-Pad and Duel Gazer probably refer to these facts.
Luna appears to be one of the few humans who can hold a "Number" card without being possessed by it. The pendant which she wears on her chest is possibly another of Dr. Faker's creations; by pressing it, Luna was able to deflect Kaito's Photon Hand, as well as teleporting herself, Shark and Yuma in an instant to a far distance.
Luna previously worked on Dr. Faker's side, assisting him, but later betrayed him. In a flashback, she is seen watching when Shark was unfairly disqualified from a tournament, taking the blame for Kyoji Yagumo. She seemed to be working on the tournament (which was sponsored by Mr. Heartland) as part of its staff.
One night, when Shark walked down an alleyway, Luna approached him, hiding her identity beneath a cloak.
She soon reveals and introduces herself, and says that Shark can call her an emissary from the moon. Shark replies saying that looks like something straight out of a fairy-tale, but that he doesn't hate them though. Luna says that she doesn't have any rancor against him, but that she must face him. Then, they begin a Duel.
The Duels ends quickly, with Shark defeating Luna in an O.T.K. After he wins, Shark asks Luna if she is alright; she is impressed that Shark could Summon 3 Xyz Monsters at once during the Duel, and says that she wasn't wrong. Luna reveals she is a Number Hunter whose goal is to eliminate the "Numbers", and says that Shark is the only one who can stop Dr. Faker, and for that he needs the power to do so - a "Number". Shark declines, saying that he was already once possessed by a "Number", and that he cannot do so. However, Luna replies that Shark knows how terrifying a "Number" can be, and that this is just why it would be okay. She further explains that "Numbers" are mirrors that reflect the hearts of the people, and at that time, his heart was full of darkness, but Yuma and Astral freed him from that darkness. She then gives Shark a mysterious card, and says that that's a new power to protect him.