Shí Hóu (石猴)
Meaning the "Stone monkey". This refers to his physical essence, being born from a sphere of rock after millennia of incubation on the Bloom Mountains/Flower-Fruit Mountain.
Měi Hóuwáng (美猴王)
Meaning "Handsome Monkey-King", or Houwang for short. The adjective Měi means "beautiful, handsome, pretty"; it also means "to be pleased with oneself", referring to his ego. Hóu ("monkey") also highlights his "naughty and impish" character.
Sūn Wùkōng (孫悟空)
The name given to him by his first master, Patriarch Bodhi. The surname Sūn was given as an in-joke about the monkey, as monkeys are also called húsūn (猢猻), and can mean either a literal or a figurative "monkey" (or "macaque"). The surname sūn (孫) and the "monkey" sūn (猻) only differ in that the latter carries an extra "dog" (quǎn) radical to highlight that 猻 refers to an animal. The given name Wùkōng means "awakened to emptiness".
The title of the keeper of the Heavenly Horses, a punning of bìmǎwēn (避馬瘟; lit. "avoiding the horses' plague"). A monkey was often put in a stable as people believed its presence could prevent the horses from catching illness. Sun Wukong was given this position by the Jade Emperor after his first intrusion into Heaven. He was promised that it was a good position to have, and that he, at least in this section, would be in the highest position. After discovering it was, in actuality, one of the lowest jobs in Heaven, he became angry, smashed the entire stable, set the horses free, and then quit. From then on, the title bìmǎwēn was used by his adversaries to mock him.
Qítiān Dàshèng (齊天大聖)
Meaning "GREat Sage, Equal of Heaven". Wùkōng took this title suggested to him by one of his demon friends, after he wreaked havoc in heaven people who heard of him called him GREat Sage. This is pronounced in Japanese as seiten-taisei ("GREat sage", dàshèng and taisei, is a Chinese and Japanese honorific). The title originally holds no power, though it is officially a high rank. Later the title was granted the responsibility to guard the Heavenly Peach Garden, due to the Jade Emperor keeping him busy so he won't make trouble.
Meaning "ascetic", it refers to a wandering monk, a priest's servant, or a person engaged in performing religious austerities. Xuanzang calls Wukong Sūn-xíngzhě when he accepts him as his companion. This is pronounced in Japanese as gyōja (making him Son-gyōja).
"Victorious Fighting Buddha". Wukong was given this name once he ascended to buddhahood at the end of the Journey to the west. This name is also mentioned during the traditional Chinese Buddhist evening services, specifically during the eighty-eight Buddhas repentance.