What is the Sharia ruling for a woman who married a Muslim man and took his family name, then learned that this is impermissible, and if her father's well-known name is that of the family who adopted him, and his real family name carries a meaning contrary to Sharia, should she attribute herself to the name of the family who adopted her father, or continue to attribute herself to her husband's family name, or take a special name for herself?

A woman is not permitted to ascribe herself to her husband's family, nor is anyone permitted to ascribe themselves to other than their father or their family. This is based on the Prophet's (peace and blessings be upon him) saying: "(No man who knowingly claims to belong to other than his father is not but a disbeliever. And whoever claims to belong to a people with whom he has no lineage, let him take his seat in the Hellfire)." Thus, if "Lathrop" is a real family name, it is not permissible to ascribe oneself to it. However, if "Throuber" is the name of your father's or his father's grandfather, then your ascription should be directly to your father's name, or to a general name you choose, while retaining the father's name.