There are several versions, where did the word rainbow. The authors etymological dictionary (2004 edition) tend to this version: the word "rainbow" is to reinvent the word "Raduga". This word is used in the Ukrainian language to refer to this natural phenomenon. Well, the word "Raduga", as you might guess, is the result of adding two words: "Paradise" and "arc". In this case, the rainbow literally means "motley arc".
What is a rainbow?