Is it permissible for a woman to be called by her husband's surname, or should it be added after her name and her father's surname?

It is not permissible to add a woman's name to her husband's name or his family's name and thereby forego her father's name. This is a custom of the disbelievers, and Allah Almighty has commanded that children be called by their fathers' names. The wives of the Prophet (peace be upon him) were not attributed to him; rather, they were attributed to their fathers, such as Aisha bint Abi Bakr. If a woman is attributed to her husband, it is a marital attribution, not a lineage attribution, like "the wife of Noah." In official documents, it is only stated as so-and-so bint so-and-so.