Answered by Mufti Mohammed Tosir Miah
Question:
Assalamulykum my question is that is it legal Islamically to change ones surname after marriage from fathers name to husbands name
Answer:
There are two ways to look at this question. If by changing the name you mean to attribute your lineage to your husband’s family, then that without any doubt is something unlawful and haraam in Islam.
Saaiduna Abu Dharr Ghifari 
narrates that he heard the Prophet of Allah 
say: “Any man who knowingly attributes himself to someone other than his father is guilty of kufr. Whoever claims to belong to a people when he has nothing to do with them, let him take his place in Hell.” (Sahih Bukhari p.497 v.1)
However, if it is not done for the aforementioned reason and everyone is aware of the wife’s lineage, then it will be permissible for the wife to change her maiden name to the husband’s, although best to refrain from as there is some element of imitation with immoral people.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.