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Hazuki Koyama (神山葉月)Hazuki is the mother of Mitsuki Koyama, and the daughter of Fuzuki Koyama.
In the anime, she was confident she was caring girl and wanted her and Aoi's child to be a girl, wanted to name her Mitsuki, and a child who will shine forever just like the moon. She said it seems such a waste on the music box and she wanted to give the song that the music box was playing and she named it "Eternal Snow" and that was how the song came to be. After that, the song became Route:L's signature number and Hazuki and Aoi's feelings touched everyone's hearts. In one episode, Mitsuki asked Wakaoji-sensei what her parents were like. Wakaoji said that Mitsuki was a lot like her mom. Hazuki was said to try to help out whenever she could and had a very kind heart.
Like Mitsuki, Hazuki was physically weak and often fell ill. She was also the splitting image of Mitsuki. Hazuki died when Mitsuki was a baby. Against the wishes of her mother, Fuzuki Koyama, Hazuki married the musician Aoi Koga. She ran away from home when she was pregnant with Mitsuki because her mother knew Hazuki's body was weak and Hazuki wouldn't survive giving birth to a child.
In the anime, she made very few appearances. She was seen in flashbacks attending Aoi's concert and receiving the music box Mitsuki now has from Aoi.She was carrying a girl and agreed with Takuto that Mitsuki was a perfect name. She rarely appears in the manga, only in a couple of flashbacks.
(Source: Full Moon Wiki)