Where did magic swizzle name come from? seems to be an odd name

Good marketing!: Magic swizzle medicine is a mouthwash. It is composed of 1 part viscous lidacaine, 1 part maalox, and 1 part dyphenhydramine. The name did its job--it caught your attention!

Not from a wizard: The mouthwash termed the "magic swizzle" is such because it gives relief to a painful mouth situation, therefore "magic" and you swish/spin it around your mouth much like a swizzle stick swirls a drink, hence the "swizzle." i hope this helps.