Kunyas for the Childless
Basil Dragonstrike

Anyone interested in Arabic onomastics will have come across the kunya. You are usually told this is either Abu (for males) or Umm (for females) followed by the name of the eldest son. After a bit, you will hear of "metaphorical kunyas," kunyas based on a person's habits or similar. The two examples usually trotted out are:
Abu Hurayra---"Father of a kitten", and
Abu al-ʻAtāhiyah---"Father of Craziness"

If you keep digging, you'll find eamples of Abū/Umm followed by the name of a daughter: this, though, only if there is no son. Also, this is only found in early Islam; it died out in the first couple of centuries AH.

But, what you are not likely to find are kunyas for the childless; those anywhere from newborn, to not quite yet marriageable, to fully adult but without a child. But, depending on time and place within Islamdom, this happened.

As The Encyclopaedia of Islam [1] says, "However, the kunya can be...given to a child, [although] the latter might well have no issue of its own throughout his life. The giving of a kunya can in effect act as an expression of the hope that its [b]earer will have a son and will give him a determined name"

As Annemarie Schimmel [2] put it, "...if the person was still young, the hope that they might be blessed with a child, especially a son."

As examples of this being done, let's turn to one of the works I've compiled lists of names from: the diary of Ibn al-Bannāʼ {https://s-gabriel.org/names/basil/ibnalbanna/}. Using Makdisi's scheme of numbering the entries, entry #60, written about 28 December 1068, reads, "On Sunday, the 28th...of this month, a male child was born to the Sharīf Abū'l-Ghanāʼim. He named him Masʻūd, and gave him the kunya of Abū Manṣūr.---May God favour him!"

Here's another example from Ibn al-Bannāʼ, from about 5 May 1069: "On Tuesday, the 10th of Rajab, the woman-neighbor of the Shaikh Ajall Ibn Jarada gave birth to a son,..The named him Yaḥyā, and gave him the kunya of (. . .); then they gave him the kunya of Abū ʻAlī." The (. . .) is Makdisi's way of indicating a word he can't read well enough to translate. So, on this occasion a new-born was given two kunyas!

Then in another work, Consorts of the Caliphs [3], there's a reference to Abū Isḥāq Ibrāhīm, and it's noted that he died aged 3 years old. Clearly, this is a case of a child being given a kunya.

In the collection of ḥadiths of Muhammad al-Bukhari [4], in #847, is reference to a youngster with the kunya Abu ʻUmayr. Number 848 and 849 are two forms of a ḥadith stating that a certain person named ʻAlqama was given the kunya Abu Shibl even though he had no child: note that it's not clear how old ʻAlqama was at the time, but it's clearly stated he had no chilldren.

Thus we see that kunyas for children, and for childless persons, are not unknown. So, if one wishes to portray a childless person, having a kunya is certainly possible.

[1] The Encyclopaedia of Islam, 2nd Edition, volume 5, copyright 1986 by E. J. Brill, publishers
[2] Islamic Names by Annemarie Schimmel, copyright 1989 by Annemarie Schimmel, published by Edinburgh University Press
[3] Consorts of the Caliphs by Ibn al-Sāʻi, translated by Shawkat M. Toorawa copyright 2017 published by NYU Press
[4] http://www.academia.edu/12127892/Imam_Bukha