“Despite having a written origin, Eddie had never stated the correct name of where he came from through out the show's run. The running joke often had him stating a place that did not exist, followed by an admission to misremembering it as a place he delivered to as opposed to a place he lived.”

Eddie isn’t a puppet. Eddie is trapped in a puppet like outfit and forced to play the part of a mailman in order to keep Wally et all happy. Perhaps he’s been sneaking out letters to get someone’s attention and they are only now being discovered. That’s why he keeps “misremembering places that don’t exist”, because real world cities wouldn’t exist in their world and would sound like a joke or nonsense to the Welcome Home residents. Maybe the others are too, but Eddie is definitely the most recent “addition” to the neighborhood. Perhaps he’s even the original creator, Ronald Dorelaine!