´It was narrated from Aisha that she said to the Prophet(ﷺ):` "All of your wives have a Kunyah except me." He said: "You are Umm Abdullah".
Related hadith on this topic
Explanation & Benefits
Maulana Ataullah Sajid
Benefits and Issues:
➊ The intention of the Mother of the Believers, Aisha (radi Allahu anha), was that a suitable kunyah (agnomen) should also be designated for her.
➋ The Mother of the Believers (radi Allahu anha) said this because she had no children by whose name she could adopt a kunyah.
➌ The Prophet (sallallahu alayhi wa sallam) most likely assigned the kunyah of Aisha (radi Allahu anha) in relation to Abdullah ibn al-Zubayr (radi Allahu anhu), who was the nephew of the Mother of the Believers (radi Allahu anha) and the son of Asma bint Abi Bakr (radi Allahu anha).
Source: Commentary on Sunan Ibn Mājah by Mawlānā ‘Atā’ullāh Sājid, Page: 3739
Shaykh Umar Farooq Saeedi
Benefits and Issues:
It is also permissible for women to adopt a kunyah (teknonym), whether they have children or not.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 4970