Naming baby on birth certificate. English vs Chinese

If we give our child an English name will she automatically lose the ability to be a Chinese citizen/apply for hukuo?

I’m American and my wife is from Xiamen. We just had a baby in Xiamen and have 20 days to decide a name. I want to give our baby an English name on the birth certificate since that’s what will be used on the US passport and I also want our baby to have my last name.

If we put an English name on the birth certificate, does this mean we are giving up the babies right to be a Chinese citizen? Or is there a way we can still apply for our baby to have a Chinese name/hukou/ Chinese passport ?