Fancy, different colored carp are called "nishikigoi," which literally means "brocaded carp" in Japanese.
Koi is short for nishikigoi. The story is that the word "koi' was first used by Confucius in 500 B.C. King Shoko, from Ro, gave Confucius a koi as a gift when Confucius' first son was born because carp were considered a symbol of strength.
This seems as good a story as any other.