so it's not really "west factory" or "east factory", but you know because eunuchs are called gonggong, and where they're based is the gongchang, and a factory is gongchang too, but I don't think there's any other translations for it unless you just call it, what, "west eunuch workhouse" and "east eunuch workhouse"?
https://forum.questionablequesting.com/threads/introduction-thread-sup-all.6/