It is the name they use internally, I believe even when scraping the API it comes as MonkeyKing as well.
Yep. For some reason (before my time) Wukong didn't get his internal file names changed when his name was picked, unlike all other champs. Most champions go through a lot of their development with a code name (e.g. Talon was BladeRogue, Rakan was DuoSupport). They then get renamed when we pick a final name for them. Didn't happen with all files for Wukong though for some reason.