It is narrated from Sayyida Asma bint Abi Bakr (may Allah be pleased with her) that she became pregnant in Mecca, and this child was Abdullah bin Zubair (may Allah be pleased with him). She says: When the days of pregnancy were completed, I set out from Mecca towards Madinah Munawwarah and stayed at Quba, and I gave birth to him there. I took him to the service of the Noble Prophet (peace and blessings be upon him) and placed him in his (peace be upon him) lap. The Prophet (peace and blessings be upon him) called for dates, chewed them, and put his blessed saliva into the child’s mouth. The very first thing to enter his stomach was the saliva of the Messenger of Allah (peace and blessings be upon him). Sayyida Asma (may Allah be pleased with her) says that then the Prophet (peace and blessings be upon him) performed tahneek with dates, supplicated for him, and prayed for blessings for him. In Islam, this was the first child to be born! What is meant is that this was the first child born to the Muhajireen in Madinah. Otherwise, the first child of the Muhajireen outside Madinah was Abdullah bin Ja’far, who was born in Abyssinia, and after the migration, the first child born among the Ansar was Muslima bin Mukhlad. [فتح الباری: ج۷، ص ۲۴۸] (Abdullah Rafiq)

It is narrated from Sayyida Aisha Siddiqa (may Allah be pleased with her), she says: I took Abdullah bin Zubair (may Allah be pleased with him) to the service of the Noble Prophet (peace and blessings be upon him). The Prophet (peace and blessings be upon him) gave him a chewed date and said: His name is Abdullah, and (Aisha!) you are Umm Abdullah.