When light is refracted by the different densities of hot and cold air it creates an illusion. This phenominon is known as a mirage. When light is refracted, deflected and dispersed by passing through raindrops it creates an illusion too. This phenominon has no name. I believe it should as this would help clarify the nature of rainbows.
Rainbows are created by refraction. Refraction already causes the light to shift colors, change directions, and be dispersed. Therefore, the term refraction already adequately covers the process of creating a rainbow. There is not much more that needs to be clarified, as just saying that it is caused by refraction explains it enough.