´Narrated 'Ali bin Abi Talib:` that he said: "O Messenger of Allah (ﷺ)! If I have a son after you do you think I could name him your Kunyah?" He said: "Yes." So he said: "So that was permitted for me."
Hadith Referenceسنن ترمذي / كتاب الأدب عن رسول الله صلى الله عليه وسلم / 2843
Muhammad bin al-Hanafiyyah quoted Ali as saying: I said: Messenger of Allah! tell me if a son is born to me after your death, may I give him your name and your kunyah? He replied: Yes. The transmitter Abu Bakr did not mention the words "I said". Instead, he said: Ali said to the Prophet ﷺ.
Shaykh Umar Farooq Saeedi
Benefits and Issues: From this incident, the permissibility of adopting both a name and a kunyah (patronymic) is understood. And Allah knows best.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 4967