Peppy's last name suggests that he is a hare, yet he is actually a rabbit. He has long ears, large incisors, and a country accent that seems to mellow out in each game as he gets older. In all games, he wears a long trench coat with a long collar, with inner-clothing similar to Fox McCloud, Falco Lombardi and Slippy Toad's except that it is red in color. In later games, he grows a white mustache. Peppy's original character artwork had brown fur in the original Star Fox and Star Fox 2 as well as the Nintendo Power comics, but not in the actual game Star Fox game. As of Star Fox 64 and onwards, Peppy is now grey furred, but has brown fur as of Star Fox Zero, which is a likely reference to his original, realistic character artwork in Star Fox and the unused design in Star Fox 2.
Peppy's character throughout the games and spin-off media is traditionally an advisor, making useful hints and tips for Fox to follow. In all of the games and spin-off media, Peppy is considered a father figure to Fox and the rest of the team. This is due to having been lifelong friends with James McCloud and having watched Fox grow from a young pup to an experienced pilot. Also, his daughter Lucy Hare revealed that he sees Krystal as a "second daughter". The "Peppy" part of his full name may come from his "peppy" behavior in Star Fox 64, but this is contradicted in the later games, as he gets older and slower.
In Star Fox 64, having been a prisioner of Andross, Peppy learned a great deal about the ways of the Androssian Empire and how they opperate, since he once had to escape from the planet Venom, enabling him great foreknowledge essential to winning the war.
Even though Peppy declined the position of Star Fox's leader and insited that Fox should take the title, he still gives commanding advice to which other characters respond likely to due to his seniority. In his senior age Peppy appears to have a gentle nagging side and has no approval for tomfoolery, evident when Slippy breaks formation or gets into trouble, or when Falco exceeds his speed. Since his retirement from active duty in Adventures, Peppy still retained his wise, senior demaner but apparently gainsed a sense of abesnt mindedness from getting more older and even falling asleep on the game's main menu until woken up by the player's selection.
In Assault, Peppy had taken a more secondary command position to go hand in hand with his advisory role, whilst making instructions and directing orders to the active team. Stages in the game also witness a more reckless side to Peppy, evident when flying an Arwing out of the blue to rescue his old friend, General Pepper from a fatal crash at his own expense, and again when flying the Great Fox into the powerful shield at the potential cost of his own life.
In Star Fox Command, when defeating the bioweapon on Titania, Peppy admits to having been afraid of Andross, which is understandable for his captivity and the presumed death of James at the Ape's doing.