What is the name of the online world where Final Fantasy XI is set?

Final Fantasy XI is set in the online world of Vana'diel.

Vana'diel is the shared fantasy setting for the game's player-created characters, nations, quests, jobs, and long-running storylines. Players explore regions, cooperate in parties, fight monsters, develop multiple jobs, and become involved in conflicts involving the world's major powers and recurring threats.

Final Fantasy XI launched in Japan in 2002 for PlayStation 2 and Windows, later reaching Xbox 360. It was the first main Final Fantasy game designed as a massively multiplayer online role-playing game, and it notably supported cross-platform play between PlayStation 2 and Windows at launch. Its subscription model and persistent world helped distinguish it from the series' single-player entries.

The most likely mix-up is Eorzea, the setting of Final Fantasy XIV. Gaia is associated with Final Fantasy IX, while Ivalice appears in several games, including Final Fantasy XII and Final Fantasy Tactics. Vana'diel also appears in the title of the 2015 concluding main scenario, Rhapsodies of Vana'diel.