Name and Lineage of Imam Tirmidhi

His name was Muhammad and his kunyah was Abu Isa. His lineage, according to most narrations, is: Muhammad ibn Isa ibn Sawrah ibn Musa ibn Dahhak al-Sulami al-Bughi al-Tirmidhi.
According to some other reports, his lineage is: Muhammad ibn Isa ibn Sawrah ibn Shaddad al-Sulami al-Bughi al-Tirmidhi — that is, instead of Musa ibn Dahhak, it is Shaddad, as mentioned in al-Sam'ani’s book *al-Ansab*.
In *Tahdhib al-Kamal* by al-Mizzi, it is recorded as: Muhammad ibn Isa ibn Sawrah ibn Sakan al-Sulami al-Bughi al-Tirmidhi — meaning instead of Musa, it is Sakan.