Abaddon was the father of Abaddon and grandfather of Abaddon, proprietor of Abaddon's Repository of Lost Treasures.
When Chakotay addressed "Mister Abaddon", Abaddon acknowledged that "The name was passed down from my father and his father before him. Not a very imaginative lot, but I'll answer to it just the same." (VOY: "Alice")
This character was only mentioned in dialogue.