Sheikh `Abd al-Wahhâb al-Turayrî, former professor at al-Imâm University in Riyadh
The woman has to keep the name of her father and not her husband. In the hadîth, the Prophet (peace be upon him) gave a severe warning to anyone who attributes himself to other than his father.
Allah says in the Qur’ân: “Call them by the names of their fathers: that is more just in the sight of Allah, but if you know not their father’s names, (then call them) your brothers in faith, or your wards.”
Due to the seriousness of the matter, if a woman has her legal documentation like her passport in her husband’s family name, then she has to change her official documents back to her father’s family name if she can. It is not enough that in her daily practice she abides by the legal ruling and people call her by her father’s name and not her husband’s. She must change her legal documentation if she can.
Source: Islam Today