Welcome to the forum!
You have a very pretty Red Double tail VT betta. He does look like he may have a little bit of fin damage so your going to want to treat him with a little aquarium salt to help him heal.
My more pressing concern is his housing. It looks like you have a "Lee's Betta Keeper" right? I use one of these as my picture tank and I recognized the plant. This tank is far too small for him. He needs a 2 gallon tank or larger, with a heater set to 76-80*F. Until you can upgrade him your going to need to do daily water changes on that tank so the ammonia levels don't harm him.
Check out the betta care sheet and FAQ at the top of this section for betta care tips