The Postman is a character found within The Legend of Zelda series, debuting in the Nintendo 64 video game The Legend of Zelda: Majora's Mask. The different Postmen that appear in the series aren't the same character, but rather they just bare the same title, similar to the protagonist of the series Link and Princess Zelda. He is one of the fastest characters in the series, known to be dedicated to getting the job done, which as his name suggests is delivering mail. While the characters' real name is probably not Postman, this is the name gamers know him by. In Majora's Mask, he is a counterpart to the Marathon Man in The Legend of Zelda: Ocarina of Time.
When the Postman in Phantom Hourglass appears for the first time, he asks the player to not shoot him with a slingshot. This is most likely a reference to Pete from Animal Crossing, whom the player can actually shoot down with a slingshot.