Is it permissible, in Islamic law, to add a tribal surname to one's family name through mediation without conclusive legal evidence, and is this considered affiliating oneself with other than one's father?

The Sacred Law has warned against an individual falsely attributing themselves to a lineage other than their true one. And whoever claims to be the son of other than his true father, while knowing that he is not his father, then Paradise is forbidden to him. Lineage is established by the testimony of two upright witnesses. If the two witnesses are upright, then it is permissible to officially establish the lineage; otherwise, it is not permissible to circumvent the law. Differentiation between people is based on piety, not lineage, and the Prophet, peace and blessings be upon him, forbade boasting about lineage.