The signature on the back of the card should be consistent with the signature on the passport. There is a SIGNITURE column on the back of the passport, where you need to handwrite your signature, which can be in Chinese, Pinyin, or even symbols. Then after leaving the country, all signatures will be as shown in the passport, so that if any problems arise, it will be easier to handle.
PS: It doesn’t matter if your last name comes after or before your first name on your credit card. When you swipe the card, you must sign the same signature as on your credit card
I am currently studying in Australia, and the application is This is how Bank of China’s combined card is made. It doesn’t matter where you are, it’s the same in the United States. The best way is to have your signature consistent with your passport signature in all places where you need to sign when going abroad. If there are any problems, because your signature is consistent with your passport, it will be easy to solve.