Historically in the Middle East, "last names" weren't really last names the way we think about them. You were known by your ancestry. Usually [Your name] son/daughter of [Father's Name] and then perhaps a tribal affiliation which almost always referred to a distant ancestor. So, for example, Aisha bint Abi Bakr at-Taymi is Aisha, the daughter of Abu Bakr, from the Taym tribe. Taym being a great-great-great-great-great-great-grandfather.

In such a system, changing names after marriage doesn't make any sense because the woman is not suddenly the daughter of her father-in-law.