Is it permissible, Islamically, for her to keep her current family name, which is the family name of her stepfather who adopted her, knowing that her mother and father committed adultery before marriage, and the questioner has never carried her biological father's family name?

The majority of jurists hold that the child of adultery is not attributed to the adulterer, while some scholars, such as Ibn Taymiyyah, permit attributing the child to the adulterer if the woman was not a firash (wife). Adoption is forbidden in Islam, which is attributing a child to other than his father, because Allah Almighty says: (Call them by [the names of] their fathers; it is more just in the sight of Allah). The correct approach is to attribute the child to the adulterer in cases of conflict, because there is a difference of opinion regarding his attribution to the adulterer, and an agreement on the prohibition of adoption.