This could be a slightly slippery slope. Even if your name doesn't proclaim your Chinese background, there may be other aspects of your application that will. For instance, if your parents attended a Chinese university or your résumé mentions Chinese language or cultural activities, then you may "out" yourself as Asian anyway. It's possible, too, that an interview write-up or teacher reference might note in passing that you are Chinese.
If this does happen, and you've omitted the ethnicity question, it's certainly not a big deal. However, it may send a subliminal message to admission officials that you are trying to game the system or to simply deny who you are. Again, it's not a deal-breaker but it's not to your advantage either.
I do agree with you, however, that Asians can be the victims of prejudice in admissions offices, especially at some of the sought-after schools. Most admission folks will not openly agree, but I stand by my opinion nonetheless. Sometimes this "prejudice" isn't based on anti-Asian feelings per se but is the result of so many Asian applications seeming very similar on paper ... top grades and top test scores, along with participation in a predictable roster of extracurriculars (orchestra, math club, chess club, Science Olympiad, tennis team, etc.). So admission committees may be most likely to say yes to those Asian applicants who are pursuing more atypical paths and who thus are more apt to stand out in a crowd. The upshot is that super students with stellar "numbers" and flawless résumés are turned away in droves and appear to be the victims of anti-Asian bias.
So I do understand your reservations about answering the ethnicity question on your applications. Certainly, no candidate who is uncomfortable responding to this question (for any reason) should feel compelled to do so. However, in your case, I would suggest that you reconsider. Not only is there an outside chance that, by ignoring it, you might actually be hurting--not helping--your admission odds, but also I suspect that, in the long run, you'll be happier with yourself if you proudly proclaim your Chinese heritage.
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