Is it obligatory to verify the correctness of one's family lineage and change it if it is proven to be incorrect, taking into consideration the difficulty of doing so for a girl who has no means of verification and does not wish to inform her father, in addition to potential social obstacles and her father's possible refusal?

All doubts must be dispelled, and reliance placed on what the father stated, as people are to be believed concerning their lineage. It is not permissible to change one's affiliation to the father or his family. Al-Bukhari and Muslim narrated from Sa'd ibn Abi Waqqas that the Prophet, peace and blessings be upon him, said: "Whoever claims to be the son of other than his father, knowing that he is not his father, Paradise is forbidden for him." This hadith indicates the prohibition of denying one's known lineage and claiming lineage to another, and this is a grave sin due to the great harms that result from it.