Um, I'm sorry, I think my only real answer is, "I don't know" =(.

I guess it depends on a lot of things, like: Why did you choose to give a background character a Westernised name? What the world of your story like? How are minorities as a whole represented in your story? Why is it important for you that the character be noticed as Chinese?

I ask the last question not as a simple "duh" question, but honestly. Is it because no one else is Chinese and you want minorities? Is it because you want the world to feel more populated with Chinese people? Is it because your heroine is Chinese and you want her to have Chinese friends? (sorry I'm totally making these up, since I don't have any idea what your story is about; they aren't meant as any sort of implications, I just can't think of anything else right now)

I really wish I had good answers, but I don't. All I can really say is: ask yourself, examine your motives, try to think of what the implications may be, and make an educated choice from there. There's really not much more that anyone can ask you to do besides that.