If a family has a TIBERIUS as a last name. It wouldn't be so bad for a boy or girl. If first name is given. The meaning and definition must correlate to that of families grit, status and history if any. It would be considerate for new fathers and mothers to really conduct some real soul searching before naming a boy Tiberius. Tiberius is a strong name, and demands a certain character to match that of parents personalities in hope that their baby may grow up acquiring mutual traits that will reflect Tiberius of its won nature. I have witnessed many names that haven't been thoroughly thought out. It's the sons and daughters that have to bear the name. So be mindful.
I liked the name enough that I named my son, Tyberious. I wanted a unique name as I was tired of seeing 7 of the same name in a classroom. I didn't know at the time it was an actual name as it wasn't in any of the baby name books I had access too and I had no internet at the time. It was amazing the amount of people who hated the name before he was born, then loved the name afterwards. He was born in 2002, and I am a Star Trek fan and it didn't click until a few months afterwards.
This is such a cool sounding name, and I especially like the association with the river. But unfortunately the Emperor Tiberius wasn't that nice of a person.