"Suck my dick and kill yourself!"
The title of "One Eye Guy" was given to this character by Alpha in an attempt to give his fellow souls a name. Even though it was rejected, One Eye Guy was the only name he was ever given and so is de-facto his name.
He is a friend of Alpha and Two Head Dude and so appears in every episode of Limbo. He was also referred to as "Brian" several times by Bejeebus but seemed to have no idea why. Bejeebus is senile so one can only assume that Brian is indeed someone else.
One Eye Guy appears in every episode of Limbo.