ANSWER:
No, she must not change her name after marriage.This is something that the Muslims picked from the Non Muslims. A woman would change her Surname into her husband’s name! THIS IS NOT PERMISSIBLE. This is imitating the Kuffar and taking out the father’s name and putting the husband’s name in it’s place is a MAJOR SIN and Allah curses whoever does this.
For example: if someone’s name is Fatima and her father’s name is Muhammad; she gets married to Ali Ahmad and she changes her name from Fatima Muhammad to Fatima Ahmad then this is completely prohibited. Prophet salla Allahu alaihi wa sallam cursed the people who change their father’s name.