A Chinese fishing pond owner is offering one of his carp "free to good home". He claims that this particular fish comes when called and knows his own name, which incidentally, is "Submarine". The fish was trained by the man's father using small pieces of food.
Of course, this would not surprise a clicker trainer! Anyone who has seen Karen Pryor training an Oscar would know just how trainable fish really are.
If you have your own pet goldfish (or carp) and wanted to try training it, Ogden Lindsley offers these tips here.
I have read several stories on the intelligence of koi, even appearing to recognize individual humans after years of absence. It would be really interesting to pursue that.