Wife taking husband’s surname after marriage?

It is narrated about the adopted son of the Holy Prophet ^sas, “We used to call Zaid bin Haritha, the freed slave of Allah’s Messenger ^sas, as Zaid bin Muhammad until the Qur’anic verse was revealed (Sahih al-Bukhari, Book 65):

Call them (adopted sons) by (the names of ) their fathers. That is more than just in the Sight of Allah.

(Surah al-Ahzab, 33:6)

A person’s lineage is a fact that does not change through adoption, marriage, or any other means. A wisdom of this command of the Holy Quran is to preserve that lineage to avoid complications that can arise, like in marriages. Allah Almighty says:

Nor has He made your adopted sons your real sons. That is merely a word  of your mouths; but Allah speaks the truth, and He guides to the right path.

(Surah al-Ahzab, 33:5)

Another wisdom for this command is to prevent people from falsely attributing themselves to a lineage and depriving the rights of others, like in distribution of inheritance. The Holy Prophet ^sas has condemned this, saying:

If somebody claims to be the son of any other than his real father knowingly, he but disbelieves in Allah, and if somebody claims to belong to some folk to whom he does not belong, let such a person take his place in the Fire.

(Sahih al-Bukhari, Book 61, Hadith 18).

These teachings apply differently depending on the different types of last names people have.

1. One type of last name is where people are known directly by the name of their father, for example, ‘Abdullah ibn ‘Umar (‘Abdullah son of ‘Umar). In this case, to take the name of someone other than one’s own father is forbidden.
2. Another type of last name is where people are known by their lineage. For example, people descended from the tribe of Quraish sometimes have Quraishi as their last name. In this case, if a woman gets married to a Quraishi, she does not also become a descendant of the tribe of Quraish, she remains a descendant of her own lineage. In these cases, it is better not to take a last name that specifically refers to a lineage that we are not descended from.
3. Another type of last name is where people are known by names that do not refer specifically to lineage. For example, many people have the last name of Ahmad. In these cases, there is nothing wrong with a wife taking the name of her husband if she chooses to. The second wife of Hadrat Mirza Nasir Ahmad Khalifatul-Masih III ^rta took the name “Nasir” as her last name.