The Chinese usually choose their own Western name (unless family give them one when they’re little or foreign friends christen them with a nickname or something.)
Some just pick something normal: Andrew, Carol, Frank, Stephanie, Alex. Others prefer something that they feel sounds classier or more exotic: Dancy, Suky, Heath, Coco, Harper, Sienna, Sandirena.
Some will use the literal translation of their Chinese name. 晶 (jīng) means “crystal” so Jing goes by the name Crystal. 黄虎 (huánghǔ) means “yellow tiger” so Huanghu goes by the name Tiger. (His last name is Wang, too, which makes it extra awesome.)
Some choose a name that sounds a little like their Chinese name. I know a Lin that goes by Jocelyn. A Lu that goes by Lulu. A Xiao that goes by Shawn. A Rui that goes by Rachel.
Some opt for what, to American ears, sounds like a random word. I have worked with a Fresh, a Reborn, a Feeling, and a women who went by the name Missing (which caused more than a few “Who’s On First” moments, I can assure you.) Actually, all of those names sound like decent rapper names, now that I think about it, so maybe they’re on to something.
Some invent their own name. A Linux system administrator at work named Xin goes by Sinux. A woman in production is called Blander, which I’ve heard tell was an attempt at the name Amanda.