I agree that it's an issue with Hollywood in general about confusing their Asian characters as well as other races/ethnicities.
However, I don't think it should be an issue in Trek. Sure, a character may be from China and have a Chinese name, but a majority of their ancestry may actually be something else. I'd like to think that the open borders and ease of travel depicted in Trek would contribute a lot to having the heritage of many characters be quite a varied mix. For my own children, their ancestry includes Slovak, German, English, Irish, Scottish, French, and Cherokee, and their varied features reflect some of that. But as I like to say, we're all-American mutts!