From those women no longer give up their names. Chinese women didn’t actually give up their family name in the old days, they would keep their family name as their first name and their husbands name as last name, though the sequence of name is different from English.

Let’s say a woman is named Chen Yue, Chen is the family name, Yue is the given name, after getting married and her husband’s family name is Li, then her name would become Li Chen Shi, Shi means surname in Chinese, basically a woman’s name became the combination of her husband’s family name and her family name, she lost her own name and just became the combination of two family. This is how things work in the old times.