He looks like a round-tail with a tear in the caudal tail. It's not a disease or anything and won't get any worse or effect his condition.
Sometime they call it "snake tongue" or something like that, guppy breeders sometimes try to get it to make their guppy's look fancier.
It won't go away as far as I know and won't effect your betta's well being.
Female's usually dont get fins that long, that's why i'm assuming he's just a male bred to be a roundtail meaning they just have shorter rounded fins rather the the regulars and crowntails (long frayed fins)