Tiberius is a Roman imperial name: Tiberius Julius Caesar Augustus was the second emperor of Rome, ruling from 14 to 37 AD. On a male dog, it's the grandest of the Roman emperor pet names: longer and more imposing than Caesar or Augustus, with a built-in Star Trek reference that makes it immediately recognizable to science fiction fans.
The James T. Kirk Middle Name
Captain James Tiberius Kirk (the T stands for Tiberius) is the full name of Star Trek's original captain. For an enormous swath of science fiction enthusiasts, Tiberius means Kirk. A dog named Tiberius in a household with Star Trek posters is honoring a very specific franchise; the Roman emperor is a secondary association for those owners.
The Roman Imperial Category
Roman emperor names appear regularly in male pet naming: Caesar, Augustus, Maximus, Tiberius. They share a quality of outsized historical authority applied to a domestic animal, the same ironic gap that makes occupation titles work, but with historical rather than professional scale. Cane Corsos and Rottweilers carry Tiberius with particular conviction.
The Counter-Reading: Five Syllables is a Lot
Tiberius takes genuine commitment to say repeatedly throughout a day. Ti-ber-ee-us at full speed. Most owners land on Tib or Tiber as the working shortform, both of which are reasonable, though neither has the imperial weight of the full name. Owners who love the name should make peace with the abbreviation before committing.