Changing Surname after Marriage in Islam
Question

I have read your responses to the following questions 2537 and 4362 concerning a wife retaining her father's name upon marriage. The verses mentioned from Surat Al-Ahzab states that adopted sons (and hence daughters) should not be called as sons of the step-fathers. 
However, how exactly does this apply to a wife simply changing her name for marriage; as she is not actually claiming to belong to her husband, but just taking his name? If it is a question of lineage, I would appreciate specific references from the Quran and hadith.
Praise be to Allah.Effects of imitating the West in naming
The effects of imitating the West in naming ourselves are many. One of them is the way in which people have got used to omitting the word ibn (son of) or ibnatu (daughter of) between their own names and the name of their fathers. 
The reason for this is, firstly, because some families have adopted children and given them their surname, so that the adopted child is called Fulan Fulan [where Fulan (=So and So) stands for a name] and their real children are called Fulan ibn Fulan (So and So the son of So and So). 
Now in the fourteenth century AH, people have dropped the word ibn or ibnatu which is unacceptable according to linguistics, custom and Shari`ah. May Allah help us.
Another effect is the habit of women taking their husband’s surnames.
Originally, the woman is So and So the Daughter of So and So, not So and So the wife of So and So! Allah says (interpretation of the meaning):
“Call them (adopted sons) by (the names of) their fathers, that is more just with Allah.” [Al-Ahzab 33:5]
As it is in this world, so it will also be in the Hereafter, as the Prophet (peace and blessings of Allah be upon him) said:
“On the Day of Resurrection, each betrayer will have a banner raised beside him, and it will be said, this is the betrayer of So and So the son of So and So.” (Narrated by al-Bukhari, 5709, and Muslim, 3265)
Shaykh Bakr Abu Zayd (may Allah have mercy on him) said: 
“This is one of the beauties of Shari`ah, because calling a person by his father’s name is more appropriate for knowing who is who and telling people apart. The father is the protector and maintainer of the child and his mother both inside and outside the home. This is why the father mixes with people in the marketplaces and takes risks by travelling to earn a halal living and strive for their sakes. So the child is given the name of the father, not of the mother who is hidden away and who is one of those whom Allah commanded (interpretation of the meaning):
And stay in your houses [al-Ahzab 33:33] (Tasmiyat al-Mawlud, 30, 31)
Changing surname after marriage
On the basis of the above, there is no blood tie between the husband and wife, so how can she take his surname as if she is part of the same lineage?
Moreover, she may get divorced, or her husband may die, and she may marry another man. Will she keep changing her surname every time she marries another man? Furthermore, there are rulings attached to her being named after her father, which have to do with inheritance, spending and who is a mahram, etc. Taking her husband’s surname overlooks all that. The husband is named after his own father, and what does she have to do with the lineage of her husband’s father? This goes against common sense and true facts. The husband has nothing that makes him better than his wife so that she should take his surname, whilst he takes his father’s name.
Hence everyone who has gone against this and taken her husband’s name should put matters right. We ask Allah to put all the affairs of the Muslims right.
For more, please see these answers: Names and Nicknames
And Allah knows best.