From the experts:
The name of an important ancient Roman emperor, Tiberius might sound a bit heavy for a modern boy to carry, but with the rise of Atticus, Tiberius and brothers begin to feel more baby-friendly, much in the same way as Old Testament names like Elijah and Isaiah have been rejuvenated.
The contemporary ear has become attuned to the name via some modern sagas. There were two Tiberiuses in the Harry Potter universe: T. McLaggen, uncle of Cormac, and T. Ogden, a former member of the Wizengamot. Peter O'Toole played Emperor Tiberius Caesar in the 1979 Caligula, and James Tiberius Kirk was Captain of the USS Enterprise on Star Trek.