Abbad bin Hamzah bin Abdullah bin al-Zubayr narrated that Aishah (may Allah be pleased with her) said: "O Messenger of Allah, will you not give me a kunyah?" He (peace and blessings be upon him) said: "Take your kunyah from Abdullah bin al-Zubayr." So she was called by the kunyah Umm Abdullah.
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 13822