This is just a martini with a different garnish, so why come up with a whole new name for it? We think it should stand as a testament to charlie connolly, henceforth known as the laziest bartender who ever lived. In the 1930s, a customer asked connolly for something different, and this is what he made: a martini with a cocktail onion, named after the customer (perhaps as an ironic scolding, for daring to order off the standard menu?) the cocktail onion really does add a certain something, though, so if you like martinis you oughta give the gibson a shot.