The Prophet ﷺ saw a lamp in Zubayr's house and said, "Ayesha, I think Asma must have given birth. Do not name him until I name him." So he named him Abdullah and softened a date in his mouth, then placed it in the child's mouth with his own hand.
حدثنا عبد الله بن إسحق الجوهري حدثنا أبو عاصم عن عبد الله بن المؤمل عن ابن أبي مليكة
أن النبي ﷺ رأى في بيت الزبير مصباحا فقال يا عائشة ما أرى أسماء إلا قد نفست فلا تسموه حتى أسميه فسماه عبد الله وحنكه بتمرة بيده
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[Its chain is daif]Abdullah bin Muammal is daif (Taqrib).Muslim (Hadith: 2146) and Bukhari (Hadith: 3909, 3910) narrated, "Asma gave birth to Abdullah bin Zubayr at Quba, then she went out to the Messenger of Allah ﷺ so that he might chew something and put it in the child's mouth. The Messenger of Allah took him from her and placed him in his lap, then called for a date... he chewed it and spat it into the child's mouth, and named him Abdullah," and this is the preserved version.