Final answer:
To obtain a martini served with a cocktail onion, a Gibson should be ordered. This distinguishes it from other martini variants, which typically feature an olive or lemon twist garnish.
Step-by-step explanation:
To get a martini garnished with a cocktail onion, you would have to order a Gibson. The Gibson is a variation of the classic martini, which traditionally consists of gin (or sometimes vodka), dry vermouth, and is garnished with a cocktail onion instead of the typical olive or lemon twist. This garnish is what differentiates a Gibson from other martinis.