Mixed dual baby names?

I'm curious: when a foreigner and a Taiwanese person have a baby, how is the naming handled? In in many Western cultures, the kid will have the Dad's last name. But if the baby is born in Taiwan to a mixed couple, it will probably get a Chinese character name. So what happens? For example, I have a Chinese name, but I'm not particularly attached to it (I got it assigned to me in an English class and it just sort of stuck). So I'm guessing if I have a kid with my wife, it's Chinese name will be her family name, which I am okay with. But It seems like most English transliterations just take the Romanization of that Chinese name. But if that were the case, my name would just sort of disappear. So does anybody have kids (or maybe you yourself) where the Chinese name and the English name are completely different?

It seems a bit strange to me that a person could be 丁維中 (Ding Wei Zhong) in Taiwan and John Smith in America. But I'm guessing this happens? Anyone have personal examples of this or how you handle this situation?