The tradition of changing a woman's name after marriage is taken from non-Muslims as there is no evidence from among the earlier Muslims of such a tradition.
It is not permissible for a Muslim woman who gets married to change her name. This is because Allaah Subhaanahu wa ta'alaa commands us to call people with their father's name.
"Call them by (the names of) their fathers: that is more just with Allâh. But if you know not their father's (names) call them your brothers in faith and MawâlIkum (your freed slaves)…" (Al Ahzab:5)
The Messenger of Allaah (peace and blessings of Allaah be upon him ) said: "Whoever claims knowingly to belong to someone other than his father will be denied Paradise." narrated al-Bukhaari and Muslim
He also said: "Whoever claims to belong to someone other than his father, will be cursed by Allaah, the angels and all the people, and Allaah will not accept any deeds or excuses from him on the Day of Resurrection ." narrated Muslim
This is also an imitation of non-Muslims as this is a tradition amongst them and was not known amongst the earlier Muslims. Imitating the non-Muslims is not permissible, especially when it contradicts an order or advice from Allaah and His Messenger (peace and blessings of Allaah be upon him).
The Messenger (peace and blessings of Allaah be upon him) said: "Be different from the mushrikeen" Al-Bukhari
And he also said: "Whoever imitates a nation, then he is from them". Narrated Abu-Dawood
However, if there is a necessity for legal reasons then the necessity would ease the rule and a woman will be able to add the surname of her husband, after the surname from her father, so if a woman's name before her marriage is Aa'ishah Ali and her husband's surname is Ahmad, then for legal necessities, she can call herself Aa'ishah Ali Ahmad.
And Allaah knows best.
