Why can a child’s surname be the same as the father’s surname and the mother’s surname?

Of course!

As long as your parents are willing! The Constitution does not stipulate that children must take their father's surname.

I know a friend whose father’s surname is Bao. He thinks the surname Bao is not nice. He has been called Baozi since he was a child. He doesn’t want his daughter to be teased like this, so he named his eldest daughter Yujing and his younger daughter Yujing. They were named Xueqing. Neither daughter had a surname, so that was the name on their ID cards. A friend said that her parents thought that a name was just a code name for a person! What enlightened parents!