BaiQiuyue yes, depending on the style of the person who's writing/translating, they can choose to separate them or not. accurately, in chinese pinyin (which is the alphabetic way of spelling out chinese characters), the letters would be separated, so separating would be the most correct if you want to get technical. however, I personally prefer to keep the first name put together into one word because that's easier to read for non-chinese speaking individuals.
but either way, both of them make bai (in your example) the surname. it's just a stylistic choice and doesn't impact the actual contents of the name very much!