The edges don't look black so I don't think it's fin rot, I'm not sure where the tear is though. It mostly looks like his caudal (butt) fin is just ragged, My old Betta had the same issue on his ventral fins, he just never properly healed from fin rot. my suggestion would be to get some melafix or pimafix from your local petstore and follow the instructions on those just in case it is fin rot. I find it also has reduced tail biting after making changes to a tank as well. (even if there's nothing really wrong it doesn't hurt the fish I add some twice a week just to prevent diseases) Also check any of your ornaments, if you added any new ones, for sharp edges as they tear the fins really easily. if his fins were ragged before it could be how he was born or he may just not have recovered from something he had.