It looks like a platty. I would just keep an eye on him, make sure that nothing else picks on him, and see if you can keep him away from lots of moving water if he is having trouble swimming.
I have had a rasbora have his back tail completly eaten by disease, have him barely able to swim, then have him come back and live for another few years after I cured the fin rot problem. It was so bad that when another fish swam by him, he spun in circles because he was in such bad shape. He was my favorite fish ever, because I loved his survival factor.
Just try and be patient with him, and make sure he does not develop any other disease like fin rot, or some sort of fungus. It is common for a fish with damage to develop another disease. Make sure that he does not get sick, and if he does, you should immediately move him to a quarentine tank to make sure he does not pass his issues to other healtier fish. As sad as it sounds, one fish is not worth your whole tank, but that is what a quarentine tank is for. Also keep an eye on your other fish because when there is a weak fish, it is also pretty common for the other fish to gang up on the injured fish and kill it.
If you do not have one, you should. An easy quarentine tank to get is a small 10g setup from like walmart for 30$ or so with filter, etc. You do not need a light, and it should come with a cheap heater/filter. If you do not have one, christmas is coming up, makes an easy gift request.
Just my advise.
Sorry for the long post. I hope it is helpful.