WE RELATE FROM the Ṣaḥīḥs of al-Bukhārī and Muslim that Anas 
said: “The Prophet 
was the best of all people in character. I had a brother called Abū ‘Umayr” (the narrator added, “I think he said Faṭīm”). “When the Prophet came to him he said: ‘O Abū ‘Umayr, what did the little bird do?’ He used to play with a bird.” [1].
said: “The Prophet was the best of all people in character. I had a brother called Abū ‘Umayr” (the narrator added, “I think he said Faṭīm”). “When the Prophet came to him he said: ‘O Abū ‘Umayr, what did the little bird do?’ He used to play with a bird.” [1].We relate with saḥīḥ isnāds, from the Sunan of Abū Dāwūd and others that ‘Ā’ishah 
said: “Messenger of Allah, all of my companions have a kunyah.” He replied: “Take the kunyah of your son ‘Abdullāh.” The narrator said that he meant ‘Abdullāh ibn az-Zubayr, who was the son of her sister Asmā’ bint Abī Bakr. ‘Ā’ishah was given the kunyah ‘Umm ‘Abdullāh’. [2].
said: “Messenger of Allah, all of my companions have a kunyah.” He replied: “Take the kunyah of your son ‘Abdullāh.” The narrator said that he meant ‘Abdullāh ibn az-Zubayr, who was the son of her sister Asmā’ bint Abī Bakr. ‘Ā’ishah was given the kunyah ‘Umm ‘Abdullāh’. [2].We also relate from the book of Ibn as-Sunnī that ‘Ā’ishah said that a child of the Prophet was miscarried and he named him ‘Abdullāh, so he gave [‘Ā’ishah] the kunyah ‘mother of ‘Abdullāh’ [3].. This is a weak hadith.
said that a child of the Prophet was miscarried and he named him ‘Abdullāh, so he gave [‘Ā’ishah] the kunyah ‘mother of ‘Abdullāh’ [3].. This is a weak hadith.Numerous Companions were given a kunyah before any child was born to them, such as Abū Hurayrah and Anas Abū Ḥamzah, and so were innumerable other Companions and Tābi‘ūn after them. This is not disapproved of and is desirable, if the conditions mentioned above are fulfilled.
and Anas Abū Ḥamzah, and so were innumerable other Companions and Tābi‘ūn after them. This is not disapproved of and is desirable, if the conditions mentioned above are fulfilled.References
[1] Al-Bukhārī (6203) and Muslim (2150).
[2] Abū Dāwūd (4970).
[3] Ibn as-Sunnī (419).