Does the Imam assign a Kunya to his child immediately after birth, or during childhood, and is there a Hadith that suggests that in Al-Kafi?
We have Hadeeth evidence encouraging naming our children before their birth. ( Wasa'il al-Shia, V. 15, page 121). The Hadeeth is narrated from Imam Jafar Al-Sadiq (AS) from his fathers from Ameerul Mo'mineen Ali (AS). The Prophet Muhammad (SAWA) named his grandson Mohsin before his birth. This Hadeeth was also narrated by Shaikh al0Sadouq in his book Al-Khisal.
Wassalam.