The most famous of the Horatii was his nephew, Publius Horatius Cocles, who held the Sublician bridge against the army of Lars Porsena circa 508 BC.
The historian Livy states that most sources assigned the Horatii to Rome, and their opponents, the Curiatii, to Alba Longa.
The victory of the Horatii was a pretext for the destruction of Alba Longa, and the transfer of its noble families to Rome.
No other praenomina are found in epigraphic sources, with the possible exception of a single instance of Titus, but the reading of this inscription is uncertain.
[1] Of these, Barbatus and Pulvillus were cognomina designating different branches of the family, while Cocles appears to have been a personal surname, or agnomen, given to the hero of the Sublician bridge.