I found a very clear, and valid answer by a student of knowledge at Darul Iftaa Institute, Hisham Dawood, approved by Mufti Ebrahim Desai.
"In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
The misconception of the impermissibility in adopting the husband’s last name stems from misunderstanding the purport of the Qurānic order to attribute one’s lineage only to his/her father. In order to dispel this misunderstanding, a thorough understanding of the background of the Āyah is necessary
When Nabī Sallallāhu ‘Alaihi Wa Sallam adopted Zaid bin Ĥārithah Radillāhu ‘Anhu, he (Sallallāhu ‘Alaihi Wa Sallam) took him to the Ka’bah and proclaimed, “O People! Bear witness that Zaid is my son. I shall inherit from him and he shall inherit from me.” This practice was common amongst the Arabs. They treated their adopted children as their own; in lineage, inheritance, marriage, etc. As such, Zaid Radiallāhu ‘Anhu would be referred to as Zaid bin Muĥammad. However, when the following Āyah was revealed, the Saĥābah would call him Zaid bin Ĥārithah
وَمَا جَعَلَ أَدْعِيَاءَكُمْ أَبْنَاءَكُمْ...ادْعُوهُمْ لِآبَائِهِمْ هُوَ أَقْسَطُ عِنْدَ اللَّه (الأحزاب ٤،٥)
“And He (Allāh) has not made your adopted sons your real sons…Attribute them (adopted children) to their father. This is more just according to Allāh” (Al Aĥzāb 4,5)
Hence, the prohibition which was revealed was in the context of the practice of the Arab society i.e. considering the adopted child to be the adoptive father’s biological child by attributing his lineage to that of the adoptive father. Ultimately, the verse prohibits rejecting one’s lineage or ascribing it to another.
This is corroborated by a Hadīth in Saĥīĥ Al Bukhārī:
إن من أعظم الفرى أن يدعي الرجل إلى غير أبيه (صحيح البخاري ج-٤ ص-١٨١، دار المنهاج)
“One of the biggest lies is that a person attributes his lineage to other than his biological father”
Thus it is clear that false genealogical attribution is prohibited in Qurān and Sunnah, and not any other type of identification.
The impermissibility for a woman to adopt her husband’s last name ... is based on the following arguments:
The Qurān and Sunnah do not “require” or command women to adopt the husband’s last name.
The wives of Nabī Sallallāhu ‘Alaihi Wa Sallam did not adopt his name. They kept the names of their fathers, though they (their fathers) were Kuffār.
The last name is an indication of one’s father, and represents his/her lineage.
Calling a person by his father’s name is more appropriate for knowing who is who and telling people apart.
There are rulings attached to the woman being named after her father, which have to do with her inheritance, spending, and who is her Maĥram, etc. Taking her husband’s last name overlooks all that.
We will be called by our father’s name in the Hereafter as well.
The writer claims impermissibility of adopting the husband’s last name. However, none of the proofs reflect this claim. Whilst we agree that a woman is not “required” to alter her maiden name, the issue is not about whether or not maiden names are a requirement of Sharī’ah. The issue at hand is about whether altering maiden names is permissible or not. Proving non-requirement is not tantamount to proving impermissibility. A simple example to illustrate this is that wearing new clothes to perform Salāh is not a requirement in Sharī’ah, although it is permissible. Similarly, proving that maiden names were not altered at the time of Nabī Sallallāhu ‘Alaihi Wa Sallam does not prove impermissibility. For example, cars were not used as a mode of transport at the time of Nabī Sallallāhu ‘Alaihi Wa Sallam. That does not mean we are not permitted to use cars today.
The writer also claims that a last name is an indication of one’s father and represents one’s lineage. However, a brief analysis of a worldwide pattern even amongst Muslims will reveal that a last name is only a family name, not the father’s name. Last names represent individuals associated to a family. In the case of a woman adopting her husband’s last name, it simply indicates that she is married into such and such family.
How does adopting the husband’s last name “overlook” the laws of inheritance, spending, and Maĥramiyyah? Perhaps the writer feels that a woman will not be able to inherit from her siblings, father, etc. because she will have no proof of being from the family. If this argument is to be accepted i.e. the husband’s last name proves to be an obstacle in claiming inheritance from one’s genealogical family, then one’s family name equally stands as an obstacle in claiming inheritance from one’s husband, children, mother, etc. The same goes for spending and Maĥramiyyah.
There is no correlation between Allāh Ta’ālā calling us by our father’s name on the Day of Judgment and the impermissibility of adopting the husband’s last name. Being called by our father’s name on the Day of Judgment does not indicate impermissibility of altering one’s maiden name in this world. The procedure adopted in the hereafter does not become law for worldly procedure.
The practice of our pious predecessors illustrates that adopting methods of identification other than attribution to one’s father is not inconsistent with the Shar’ī command of attributing one’s lineage only to his/her father. Many Saĥābah, Tābi’een, and ‘Ulamā were even “attributed” to their mothers/grandmothers. For example,
‘Abdullāh ibn Umme Maktūm (one of the muezzins of Rasūlullāh Sallallāhu ‘Alaihi Wa Sallam),
Sakhr ibn Al ‘Ailah,
Ibn Al Lutbiyyah (Radiallāhu ‘Anhum),
Muĥammad ibn Al Ĥanafiyyah (son of ‘Alī Radiallāhu ‘Anhu),
Ibn Mājah (Sāhib Al Sunan)
Ibn Taimiyyah (Aĥmad ibn ‘Abd Al Halīm), etc.
Why didn’t these luminaries attribute themselves to their fathers only? Were they not aware of the Qurānic order?
It is clear that the command in reference is the prohibition to deny a biological attribution and not to prohibit every other form of attribution.
It is best that the husband’s last name is adopted with mutual consent. If there is a need for the wife to adopt her husband’s last name, it is up to the husband to convince her to do so.
And Allah Ta’āla Knows Best"