How sound is the naming of Abraha al-Habashi's elephant as "Mahmud," and has a sound hadith been reported to that effect?

It has not been authentically reported from the Prophet (peace be upon him) or his Companions that the name of Abraha's elephant was "Mahmoud." However, the majority of biographers and exegetes have explicitly stated this, including Muqatil ibn Sulaiman, Ibn Sa'd, al-Azraqi, Ibn Jarir al-Tabari, and Ibn Kathir.

Scholars have pointed out that the mention of this name in biographies does not require prophetic authentication, and leniency is permitted in the chains of transmission for such historical matters because they do not pertain to legal rulings or doctrines, and are considered closer to anecdotes and rare occurrences.