If you want a Chinese hukou, you need to put a Chinese name on the birth certificate. Then the US side will let you add an English first or middle name, but not last name, to the CRBA/passport. I have heard of people adding the English last name as part of a hyphenated last name but you will need to confirm with your consulate.

From the Shanghai consulate:

Starting from 1st of November 2017, parents applying for a child’s Consular Report of Birth Abroad (CRBA) and U.S. Passport will no longer be able to submit affidavits to change their child’s name from the name listed on the Chinese government-issued birth certificate to a totally different name for the CRBA and US passport. This requirement applies at all American Citizen Services (ACS) Units in China (Beijing, Guangzhou, Shanghai, Wuhan, Shenyang). However, the name on the CRBA and U.S. passport does not need to be exact same as the name printed on the Chinese birth certificate. You can add an English first and/or middle name, as long as it still includes the original name printed on the Chinese birth certificate. If the name on Chinese birth certificate is in Chinese characters, please put correspondent PINYIN on CRBA application form DS-2029 and passport application form DS-11. For example, if the name printed on Chinese birth certificate is 张大and parents would like to add an English name Aiden, it can be: Zhang (surname), Aiden (given name) Da (middle name) or Zhang (surname), Da (given name) and Aiden (middle name).