They will eat many plants, volume is the key to keeping certain plants in koi ponds. We use a lot of floating plants, hornwart, parrotts feather, Phyllanthus fluitans, Ceratophyllym demersum, Limnobium laevigatum... I also add crypts, lotuses and hygrophilas but they often get nibbled up pretty bad, it's all good for them though. The floaters we use a lot because we have a lot of birds that prey on the fish. Anubias, ferns and most bog plants will also do well and shouldn't get eaten. Depends on your climate too, we have to replant everything each spring due to the cold winter, just the bog plants survive the winter, we leave the bulbs in their pots and hope for the best
Good question... I think Koi is about as scientific as it gets
Being fancy carps the full name would be Koi Cyprinus carpio, then there are all the codes given to particular strains and such.... but I don't know if "Koi" itself is a common name for something else. Probably a Japanese name