To me it looks like a silver butterfly koi

You are lucky enough to have the common version of a silver dragon koi.
these fish are characteristic because they have little whisker/protrusions around their mouths that some think look like little curly beards. (i always laugh when i think of a bearded fish)
their fins are elegant and flow well with current, but also are distinctly and very well controllable by the koi. the dorsal fin is small and low, yet somewhat able to be raised. the anal fin is very straight, but the fin membrane in it is skirt like and wavy. what gives your fish away is the tail-dragon koi have that specific rolling lyre tail pattern that is seen as a very simplistic, living art form. there are two lobes to the tail, a top and a bottom that are usually rounded.he middle of the fin is very fluid in motion and also very beautiful to watch. the coloration also can be a hint. the common variety of dragon koi have a few round, dark patches divided in half across the top of the fish and most times, the dorsal fin.
the rare version of your fish have the same features, but they are much more pronounced and have a guaranteed family history.
although a koi, the common variety do not get as large as the rarer ones, and therefore will be suited to a decently sized pond or a 180+ gallon tank
again, beautiful.

Think about building a pond or selling it to someone with a pond, as this fish will get big quickly and will probably suffer in a fish tank. Koi are simply too big for aquariums, unless they are truly enormous tanks.