The Kunyah is for the Oldest Son
Question :
Can we designate for someone the title "Abu (father of) Muhammad" even though that person has neither a wife nor children?
Answer:
It is allowed for a man or a woman to use such without having any children, for relations that are less important than this. Like the case of Abu Hurairah, may Allah be pleased with him, [which means father of a cat, a title that was attached to him because he used to have a cat that he carried with him. Likewise, it is permissible for a young person who is not married to take a Kunyah, by using his father's name or any other name. However, it is better to be clear in this matter, by taking a Kunyah using one's oldest son. Nevertheless, one does not have to do this; the Messenger of Allâh ﷺ used to call 'Aishah, may Allah be pleased with her, Umm 'Abdullah (the mother of 'Abdullah), even though Abdullah bin Az-Zubayr was her sister's son.
Source:
Ibn Jibreen
Fatawa Islamiyah, Vol. 8 Pages 212-213
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