The Epistles of John are called that because Christian tradition says they're written by—you guessed it—a guy named John. Of course, this isn't just any random 1st-century dude. This is the same guy who's said to have written the Gospel of John.
He really gets around.
The weird part is the author never names himself in either the fourth gospel or any of these three letters, so scholars can never actually be sure about who wrote these books. But since there's lots of theological overlap between John's Epistles and John's Gospel and everyone just sort of liked this idea a long time ago, the name sort of stuck.