The word entered English in the late fourteenth century from the Old French carpe.
That came directly from Vulgar Latin carpa--which led to the Italian carpa and the Spanish, uh, carpa.
It all seems to go back to the German, as the carp is originally from the Danube. The Online Etymology Dictionary speculates that the German source may be *karpa, because of the Middle Dutch carpe, the Dutch karper, the old High German karpfo and the german karpfen.
Lithuania borrowed the word, hence karpis. So did Russia, breaking boundaries by calling it karp.
So a carp, in a lot of other languages, is still basically a carp.
Except occasionally, when it's a goldfish.