Is it permissible for a tribe to claim affiliation with another tribe that shares the same name and has a known lineage tracing back to Abu Bakr Al-Siddiq (may Allah be pleased with him), especially when it is impossible to ascertain their original lineage?

Family and tribal names are derived from the names of ancestors, and similarities are common. The mere similarity of your clan's name to another clan's name is not proof of kinship between you, because a Muslim is commanded to follow knowledge, not delusions, as Allah Almighty said: (And do not pursue that of which you have no knowledge. Indeed, the hearing, the sight, and the heart - about all those [one] will be questioned). Therefore, it is not permissible to attribute your clan to a certain tribe without knowledge and clear evidence. The salvation of a servant depends on their good deeds, not on their lineage; the Prophet, peace and blessings be upon him, said: (And whoever is slowed down by his deeds, his lineage will not hasten him).