Abbad bin Hamzah bin Abdullah bin al-Zubayr narrates from Sayyidah Aishah (may Allah be pleased with her) that she said: O Messenger of Allah (peace and blessings be upon him), why do you (peace and blessings be upon him) not give me a kunyah, when all your (peace and blessings be upon him) wives have kunyahs? He (peace and blessings be upon him) said: "Take it after your son Abdullah." So her kunyah was Umm Abdullah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الضحايا / 19335