Whoever gave Ernest Evans his nick stole the idea from Fats Domino.
Blame Dick Clark who took a man who was pushing a broom and got him to cover Hank Ballard's song The Twist before it could become a hit. Dick hated Hank Ballard and his "dirty songs" so he found a sound-alike performer. Chubby's cover sounded enough like Hank's original that Hank did a double-take when he heard it on the radio.
It was Clarks wife who completed his recording name. There was already a Fats Domino, so why not continue the game theme? Because of the Clarks, the world was introduced to a singer named Chubby Checker.