Leviathans, unlike demons, do age over time albeit very slowly. While Levi and Ave appeared to be in their early to mid twenties in the flashback, Levi has aged over the centuries since and now appears to be in his early to mid thirties.
Since Leviathans do age, and will eventually die, the position of leader of the Leviathans, commonly referred to as The Leviathan, is passed down over generations. The Leviathan bears the Archon Ring as a symbol or their rule and is the only of their species that possess the full powers capable of a Leviathan. The Leviathan is a hereditary position, typically passed to the first born child of the current reigning Leviathan at their death or abdication due to old age.
Leviathans, contrary to common mortal belief, are not a singular entity but rather an entire species and the native inhabitants of the Mortal Realm, pre-dating humans by at least thousands and thousands of years. The Leviathans were enslaved by Baeozorath during his quest for absolute power over the realms and sealed away in a lowly realm by him.
Since Baeozorath would typically only bring one Leviathan to the mortal realm in his attacks on humans, it became a common idea that there was only one. Though it must be said that the myths of dragons and other great monsters do have their roots in the Leviathans.
After the Leviathans were freed by Hell, they decided to remain in their new realm and make it their home, leaving the mortal realm to humans. The Leviathans are exceedingly powerful, their true forms generally appearing as great dragons All Leviathans are capable of adopting a human-like form though they are generally much taller than typical mortals, averaging around 7″ tall.