There are different narrations about the real name of Abu Talib (AS).
1. Some say that his name and Kunyah is same : Abu Talib. (Al-Mustadrak Alal Saheehayn byAl-Haakim Al- Nisaboori Vol 3, P 103).
2. Some say that his name is Shaybah ( Ibn Asaakir in Tareekh Dimishq V 66, P 309). But this claim is very weak among the scholars.
3. Some say that his name is Imran (Ibn Shahr Ashoob in Al-Manaqib 3:43, and Ibn Onbah in Omdatul Talib P 20) and other scholars.
4. Some say that his name is Abd Munaaf and they take the evidence from the will of his father to him in poetry which is narrated in many books like tareekh Al-Ya'qoobi, V 2, P 13, Al-Manaaqib by Ibn Shahr Ashoob 1:34, Al-Fadhaa'el By Ibn Shathaan Al-Qummi 45, Omdatul Taalib by Ibn Anabah 21 and others.
It is possible that his name was Imran and Abd Munaaf , as the society of that time used to give more than one name like Ali and Haidarah were two names for Ameerul Mo'mineen Ali (AS.