Quintillus

I actually think this name was derived from Latin 'quintilus' meaning "(the) fifth month." See also my entries in the Submitted Names Database, namely Quintilius and Quintilianus.

While the explanation in my previous comment (from the year 2008) remains somewhat feasible (or just noteworthy), it is probably far more likely that the Roman cognomen Quintillus is actually derived from the given name Quintillus, which is a diminutive of Quintus. After all, -illus is a Latin diminutive suffix for males, with -illa being the feminine equivalent (for this, compare names in the main database, such as Domitilla, Drusilla, Lucilla, Petronilla and Priscilla).