if you study other language,you have to make a other language's name?

In chinese school, we must study english. our english teacher always say "you guys have to make a english name "

I always think yes, study other language should have a other language's name.but when i came to the campus,i changed my mind.

In the US. lot of japanese don't have english name.  Why? they don't want to into the American society? in internet,someone tell me ,beause they don't need change their name to into the American society.Japanese are proud of their own culture.so i thought, yeah.although,my names have some tone is difficult for someone who didn't speak  my language, but i shouldn't let me adapt to others，i should let others adapt to me. beause,my name is my family,my language,my country given me a gift. i should be proud of my name.

do you think i'm so serious？ maybe just a name ,never mind. tell me you think.

ps. i know my English have some grammatical errors.i'm sorry for that. : )