In the fictional Gundam universe, the Tivvay class seems to be an update to the older Chivvay class cruisers. These ships are designed around MS transportation and combat. These vessles are lightly armed when compared to other Zeon ship classes, sporting only two beam turrets and a handful of missle launchers. The only known vessle is the Graf Zepplin, which appeared in Gundam 0080. This ship served as a flagship for Captain Von Helsing (no relation to the vampire hunter) and his small Zeon taskforce, who were dispatched to launched a diversionary attack on Side 6 to allow the Cyclops team entry. Later, this vessle and two Musai class ships were used to ferry nuclear arms to Side 6.
In most science fiction universes, a ship's class will generally be named after its first ship, known as the class leader or pathfinder.
Classes of starships, like their terrestrial counterpart, are used to save effort and money - it's considerably easier and cheaper to build multiple units to the same set of plans than to develop a new unique plan for every individual starship.