Cleric of the party is asked to exorcise a local demon/ghost in a villlage that has been haunting them. The cleric actually accomplishes it but the locals still "see" it around and see damage it continues to do. They are convinced that unless the cleric visits the church of Saint Duncan and uses his power and name that the cleric couldn't have possibly gotten rid of the spirit that plagues them.
Great story - I agree with other posters - solid, has a history about it.
Another thought is that this would integrate into some kinds of Sci Fi quite well - I'm thinking of Dark Heresy in particular. There are religious traditions buried in that (the Ordo Hereticus and so on) where this would fit - fight Chaos and so on.
In a more mundane way, remove the supernatural and give him the role of a local priest or some other reason to be popular - e.g. resistance to the government? Clues there in the refusal-to-politic part of the story.
Anyway, great and very useable character.