Origin: Japanese, Greek, Ukrainian
Meaning: I've come across this name as being a Japanese masculine name, the name of deceased horse breeder Zenya Yoshida, as well as the name of some minor characters in games. It also seems to be a Japanese word, either meaning "night, evening" or "eve", though whether the name is derived from the word I can't say. There could also be other meanings depending on the kanji used.
Zenya is also a variant spelling of Zenia, itself a variant of Xenia, a Greek feminine name meaning "hospitality".
I've also seen it listed as being the Ukrainian form of Zinoviya, the Russian form of Zenobia meaning "life of Zeus".