Technically speaking, this is a "Cyprinnis Carpio Domesticatus".... or simply, a domesticated Carp, aka Longfinned Koi. It is not a Goldfish (Cyprinnis Cyprinnis) as its body is not deep enough. BTW, although Goldfish and Carp, domesticated or wild, can interbreed, it's not that common, and the offspring are not viable.

Another bit of trivia; When you see one Koi with long fins and bronze coloration, and another with normal fins, but bright color, these are still the same species. The difference is about like that between a Black lab and a Rottweiler, both still Canines.

Peace,
Fish