Some people say that it is not permissible for a wife to adopt her husband's surname.

Answer

The prohibition in the Hadith applies to a person who commits deception. He deceives people regarding his lineage by assuming the surname of someone to whom he is not related then creating the idea that he is the son, etc. of that person. On the other hand, a woman takes on to her husband's surname for the sake of convenience, not for deception. No one is deceived by her new surname.

Will it be permissible to say about your wife that "She is the wife of Zaid"? Of course it is permissible. Now instead of saying to everyone that she is "the wife of Zaid", it is said for simplification: Mrs F. Zaid.". This is all what is meant when a woman adopts her husband's surname. She only says that she is the wife of so and so.