His full name is Monkey D. Luffy, or モンキー・D・ルフィ. You often hear others (particularly enemies) call him "Straw Hat Luffy" (麦わらのルフィ) or just "Straw Hat" (麦わら). Some enemies also call him あのゴムゴムの野郎, "that rubber guy", because he ate the ゴムゴムの実, the "rubber-rubber fruit", which makes him both incredibly stretchy and unable to swim. He often says of himself that he is 海賊王になる男, "the man who will become the Pirate King".
If you open "Community Lists" (it's under "Resources") and search for "One Piece" you'll find quite a few user-made lists of words and expressions that appear in One Piece. They're really fun!
