Why was Lady Fatimah bint Hizam, may God be pleased with her, given the title Umm al-Banin?

Perhaps the questioner means Umm al-Banin al-Kilabiyyah, the wife of Ali (may Allah be pleased with him). She was not a Sahabiyyah (female companion of the Prophet). Ali married her after the death of Fatimah, the Prophet's daughter. She bore him Al-Abbas and his brothers: Uthman, Ja'far, and Abdullah, all of whom were killed with their brother Al-Hussein in Karbala. We have not come across anyone who named her Fatimah, nor anyone who mentioned the reason for her kunya (teknonym) as Umm al-Banin.