"Why do you use an English name?"
"Why do Chinese people have to get an English name?"
Is it because English culture is much better or more powerful than Chinese culture?
No. The reason is simple: Chinese is too hard. A lot of Chinese speakers understand English, but a lot of English speakers don't understand Chinese at all. Anyone who cares about most people's convenience will use an English name as well.
There's no need to feel hurt or sad for using an English name. If Chinese is easy to learn and use, most people on Earth will choose Chinese! Who can blame a cultural choice like this?