Eragon didn't see the truth about himself in his true name because it has nothing to do with his morality, only his fate, so it doesn't depend on and isn't affected by whether or not he's a good person. He is Wyrdskyldr, Fatebound, regardless of whether that fate is for good or ill.

Since Eragon's personality prevents him from changing his mind and thus changing his preconcieved notions, Eragon will always proceed along one track, since never questioning your actions restricts your future options and opportunities. At least that's how I interpret his true name.