She doesn't have one. None of the official Vocaloids during the Vocaloid 2 era a defined personality or relationship because that would limit the users, composers, illustrators and fans creativity.
Her personality changes with the song. So depending on the song she can be shy, kind, evil, spoiled, masochist, diva, cruel, depressed, etc...
Remember, she's a voice, not an anime character.
- See also