Praise be to Allaah.
It seems that what is meant in the question is a woman changing her family name to that of her husband after she gets married. This is haraam and is not allowed in sharee’ah, because it is not permissible for anyone to claim to belong to anyone other than his or her father. Allaah says (interpretation of the meaning): “Call them (adopted sons) by (the names of) their fathers, that is more just with Allaah…” [al-Ahzaab 33:5]. The Prophet (peace and blessings of Allaah be upon him) said: “Allaah has cursed the one who claims to belong to someone other than his father.” (Reported by Imaam Ahmad and others). And Allaah knows best.
Sheikh Muhammed Salih Al-Munajjid