There's no such thing as a Chinese alphabet so you can't write 'JW' in Chinese.
Justin can be pronounced Jia-si-ting and written 賈斯汀 in traditional characters. The characters don't make up a chinese word but are used to represent foreign words.
As Aschenbach said there is no chinese alphabet, it is all a series of lines and strokes. When you ask a chinese person your name translated they will probobly tell you the closest sounds phonetically.