No — a Muslim woman keeps her own father's name and lineage after marriage, because Allah commanded, "Call them by [the names of] their fathers; that is more just in the sight of Allah" (Quran 33:5), revealed alongside the statement that Allah has not made adopted sons into real sons (Quran 33:4). This is why the female Companions are always known by their own lineage: Khadījah bint Khuwaylid and ʿĀʾishah bint Abī Bakr remained so throughout their marriage to the Prophet ﷺ. Marriage does not transfer a woman's nasab, and the Prophet ﷺ warned severely against attributing oneself to other than one's real father: "Whoever claims to be the son of a person other than his father, knowing that he is not his father, Paradise is forbidden to him" (Ṣaḥīḥ al-Bukhārī 6766). If a woman lives in a country whose paperwork automatically appends her husband's surname, she is not sinful for what is imposed on her administratively, provided she does not claim him as her father and her true lineage is not erased.
Q&A · Women in Islam
Does a woman take her husband's family name after marriage in Islam?
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.