My first thought is a delta tail, but his caudal fin looks a bit rough, so just a guess.
I would do some frequent water changes to make sure that his water is pristine, like 20 to 25% every other day. I would also add some Indian almond leaves (catappa leaves) to the tank for the tannins. The tannins that the leaves release will tint the water brown, if you can stand it. The tannins are very beneficial to bettas and have some slight antifungal and antibacterial properties, and tannins also help with stress. His caudal fin will get better and fuller with some time and good, clean water!