Abaddon had some hand in the creation of the team that arrived on the Island. He is seen explaining to Naomi her mission to transport the other team members onto the Island, and to look after them. He explains that, despite her objections, every member of her team was chosen for a specific reason. When Naomi asks what she should do if they encounter survivors from Oceanic 815, Abaddon reiterates ominously that there were no survivors, and repeats her assignment, making sure she is up for the task. (4x02)
When Hurley is back at Santa Rosa Mental Health Institute after getting off the Island, Abaddon pays him a visit. He tells Hurley that he is an attorney for Oceanic and offers to "upgrade" him to a nicer hospital. When Hurley becomes suspicious, Abaddon asks him, "Are they still alive?" He abruptly leaves when Hurley becomes agitated. (4x01)
A number of sources suggested based on casting information that this character was to be named "Arthur Stevens".  When asked about the subject, the producers said that fake names are used and fake scenes are read for characters to preserve secrecy.
We actually [have] the actors read fake [scenes] and give them fake character names because those casting [pages] travel so widely, there's no way to maintain secrecy. So we basically have to come up with fake but analogous scenes that will show us qualities of an actor but won't give away what the role is. So yes, the stuff out there is not totally accurate.
"Had Abaddon" was a proposed name for the Imperial capital which appeared in early drafts of Return of the Jedi.
"Abaddon" is the name of the biblical Angel of the Abyss (Revelation 9:11). The name is Greek for "destruction" or "the destroyer". As a place, it is likened to Sheol or hell.
The name is rendered in Greek as Apollyon and described as king of the locusts which rose at the sounding of the fifth trumpet. "In appearance the locusts were like horses arrayed for battle; on their heads were what looked like crowns of gold; their faces were like human faces, their hair like women's hair, and their teeth like lions' teeth; they had scales like iron breastplates, and the noise of their wings was like the noise of many chariots with horses rushing into battle. They have tails like scorpions, and stings, and their power of hurting men for five months lies in their tails. They have as king over them, the angel of the Abyss; his name in Hebrew is Abaddon, and in the Greek he has the name Apollyon." (Revelation 9:7-11)
Abaddon is mentioned again elsewhere in revelations "And the fifth angel blew his trumpet, and I saw a star fallen from heaven to earth, and he was given the key of the shaft of the bottomless pit; he opened the shaft of the bottomless pit and from the shaft rose smoke like the smoke of a great furnace, and the sun and the air were darkened with the smoke from the shaft." (Revelation 9:1-2)
Abaddon is pictured as a human sized locust, and is known as the lord of pestilence. "Then from the smoke came locusts on the earth, and they were given power like the power of scorpions of the earth; they were told not to harm the grass of the earth or any green growth or any tree, but only those of mankind who have not the seal of God upon their foreheads; they were allowed to torture them for five months, but not to kill them, and their torture was like the torture of a scorpion, when it stings a man. And in those days men will seek death and will not find it; they will long to die, and death will fly from them." (Revelation 9:3-6)
In the press release for 第4季第1集 his name is spelled "Abbadon"; in the press releases for 第4季第2集 it is spelled "Abaddon".