There is this kingdom Nanyue or Nam Viet in North Vietnam and because of this, the Chinese called it Nan Hai or Nam Hai. 
South of this is the territory of Champa, which is almost as old. The is popularly known as Sea of Champa or Sea of Cham based on the main kingdom in that area. Dai Viet called it Eastern Sea.
For the Muslims it became Sea of Sanji, probably referring to Sea of Champa.
So, the case is this. World knew it as Champa Sea till Viets started subjugating Champa. China knew it as Guangdong Sea(Nan Hai). The world called it as South China Sea probably based on Japanese Minami Shina Ka. Question is, what will you call it? Nan Hai or Champa Sea?
Also, note. Nan Hai is also because it's Southern Sea - Sea beyond the Southern Limits. So, it was never China's. May be, we need to start using correct vocabulary?
But, one thing is sure. That Sea was never China's. All these claims by Chinese are just claims in an attempt to puff their chests. In fact, the same Chinese tell us of the Indian Prince Srimara who set up the Champan principality of Kauthara.
Note: The Cham word will be Tasi Cham. Probably, the West never knew of that word because Viet started the conquest of Cham Kingdom from 980s and effectively finished off the kingdom by 1500(though it lingered on till 1830s)
