Why Is John the "Disciple Whom Jesus Loved"?
The writer of the Gospel of John gives himself an odd nickname: “The Disciple Whom Jesus Loved.” In other translations, John refers to himself as the “Beloved Disciple.” We don’t know the real meaning behind the name because John provides no explanation of it. But perhaps John uses this name as a reminder to himself and others of Jesus’ loving ministry here on earth and the disciples’ call to spread the message of that love to every nation.
Source: biblestudytools.com