This is a question that I address every time I teach a class on Gospels. Many have assumed that he is John the brother of James. But the fact is, the Gospel never tells us who he is. He is anonymous. A lot of ink has been spilled over this topic. Some think that the Beloved Disciple was a real person while others argue that he is a literary device.
Mark Goodacre has posted a 12 minute podcast giving an overview of the question. While Goodacre does not contend that John wrote the Gospel, he does suggest that the author of John crafted the Gospel so that readers will identify the Beloved Disciple with John the son of Zebedee.
Goodacre teaches New Testament at Duke University. If you are not familiar with his NT Podcasts, I highly recommend them. I have used many of them as part of my online Gospels class. They can be used quite easily in a number of different settings. They are usually no longer than 10 minutes and provide a competent overview of the topic.