It is named after how the GameCube was codenamed, 'Project Dolphin.' It's also a reference to Olimar's ship, the S.S.
It has also become famous through the ability of letting people use texture hacks and change noises in Melee. Melee Perfect Falcon and Perfect Pichu videos. It has become famous through Antdgar's Super Smash Bros.
Brawl, mostly because it does not crash as often as others and it has Netplay. The Dolphin is the mainly used Wii and GameCube emulator to play Super Smash Bros. The Dolphin Emulator, with the ISO images of Melee and Brawl ready.