All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The matter is as you read in the Fatwa that it is forbidden for a woman to assume her husband’s surname as this is among the traditions of the non-Muslims that are peculiar to them and it is not permissible to imitate them in such a matter; for more benefit, please refer to Fataawa 89932 and 085803.
It is strange that the one who gave the Fatwa that you referred to through the mentioned link said that this act (a woman taking the surname of her husband) is permissible because this is among the traditions of the non-Muslims. Since, he acknowledges that this is among their (non-Muslims) traditions, so how come he is of the view that it is permissible to imitate them while the Prophet said: “Whoever imitates a people, he is one of them.” [Abu Daawood]
Moreover, if a woman bears the surname of her husband, this means that she is really traced back to other than her father, in which case the threat that is reported in the Hadeeth applies to her. Abu Tharr narrated that he heard the Prophet saying: “There is no man who claims to be the son of any other than his real father knowingly except that he disbelieves in Allaah and whoever claims to belong to some folk to whom he does not belong, then let him take his place in Hellfire.”
Ibn Daqeeq Al-‘Eed said in his book 'Ihkaam Al-Ahkaam': “This Hadeeth is evidence that it is forbidden to deny one’s known family lineage and to be traced back to someone else’s lineage, and there is no doubt that this is a grave major sin as this leads to great disadvantages.”
On the other hand, using the fact that a person may belong to his own tribe, or his country or his profession and the like to prove that it is permissible for a wife to bear the surname of her husband is a strange and wrong deduction as there is a big difference between the two cases and it is not acceptable to draw an analogy between them. For more benefit, please refer to Fatwa 118807.
Allaah Knows best.