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Chocobo Breeder
They called it Organization XIII because she wasnt a member of the Organization for long. If anyone recalls KH:CoM, no one ever referred to the Organization as Organization XIII...It was known as the Organization. This leads me to conclude that this game may have been taking place during the course, or after, CoM...She was not a member of the Organization for long, so it seems natural to conclude that after her secession from the Organization, they named it properly Organization XIII, because Roxas was a member before her, and they were confident that they only needed one Keyblade wielder.