The story of the Roman Numerals was to give the game some faux importance. The name is actually derived from a children's toy ball, one that was owned by the daughter of Lamar Hunt - who happened to be both the owner of the Kansas City Chiefs and part of the group that facilitated the AFL-NFL merger in 1966. When he saw his daughter bouncing a solid rubber ball around the house, he asked her what it was. "It's a super ball, daddy," was the reply. And, as a "bowl game" had come to mean an important post-season game in the college ranks, Hunt suggested the name to Rozelle and the NFL. They didn't go for it at first, but the informal name stuck and the third one was officially called "Super Bowl III". It was favored by sportswriters who didn't like saying "Third NFL-AFL Championship Game" constantly.
The trophy wasn't given a name until Super Bowl V, when it was called the Vince Lombardi Memorial Trophy, after the deceased former head coach of the Packers and Redskins. Unlike many other trophies, the Lombardi Trophy isn't a traveling trophy; the NFL makes copies of it for each Super Bowl.