There is a question about why Kirk's middle name was Tiberius from an in-universe perspective. The answers explain that Kirk was given the name after his grandfather (Tiberius Kirk) and that his grandfather had an interest in the Roman emperors.
But why, out of universe, was Kirk's character given the name Tiberius? Did one of the show's producers have an interest in the Roman emperors? There's some information on the choice of Kirk's last name on Memory Alpha and Wikipedia, but no explanation about his middle name. Memory Alpha makes the connection to the historical Tiberius, but it doesn't have any citations and merely provides speculation. It also says
The name might also possibly have been influenced by the maverick Roman politician Tiberius Gracchus.
If Kirk's character was given the name because of a fascination with Roman emperors like Tiberius (which seems to be the case), then why Tiberius instead of another emperor (a more influential/famous one such as Augustus, Trajan, Marcus Aurelius, Constantine, etc.)?