Is it permissible for this newly Muslim sister, who changed her family name to her husband's out of love for him and in accordance with Hungarian laws, to keep this name, especially since she was born out of an illicit relationship, her father did not care for her, her mother hates her, and changing the name again would cost her a lot of money?

It is forbidden for a wife to attribute herself to her husband's name or his family, due to the generality of the evidence prohibiting a person from attributing himself to other than his father, such as the Almighty's saying: (Call them by [the names of] their fathers; it is more just in the sight of Allah), and what was narrated by Al-Bukhari and Muslim: "There is no man who claims to be the son of other than his father, while he knows him [his true father], except that he has committed an act of disbelief." Therefore, it is necessary to change the name. If she is unable to do so, there is no blame upon her. If she is able, let her change her name to her mother's name and her family's, for her lineage to her mother is correct, and it is not permissible for her to be attributed to her illegitimate father. Her dislike for her mother does not prevent her from correcting her lineage, for her mother has a great right to righteousness and kindness, even if she were a disbeliever, and it is recommended to pray for her guidance.