Are there names in Chinese for craters and other features on the Moon? Or are English/International names used instead?
If you are talking about the name of the craters on the moon, I would say international names are used, just like the naming of the stars.
By the way, some craters are named after Chinese people, like 万户撞击坑 and so on.
If you are talking about the features in general, we do have names for them
陨石坑 - crater
月海 - lunar mare
月相 - lunar phase