Mary Magdalene (named) reports the empty tomb to Peter and the Beloved Disciple in chapter 20, verse 2. That would seem to make it unlikely that she is the Beloved Disciple.
Also, whoever the Beloved Disciple is, that person is credited at the end of the book with writing the book (which is presumably why we call it the Gospel of John, since John is the most common identification of the Beloved). So whoever it was seems to have picked that title for him- or herself, rather than covering up someone else’s name.
Usagi
Richard Bauckham (in Jesus and the Eyewitnesses) has an interesting thesis that the writer of the Gospel of John was not John the Apostle, but John the Elder, a well-known figure in the Early Church and a mentor to Papias and others. John was not an Apostle, but a disciple from very early on - possibly the young man who escapes without his clothes at the arrest of Jesus.
Bauckham points to the Gospel writer’s use of a common ancient literary technique called “inclusio” to show that his own witness (he is the first and last person mentioned in the Gospel) can be relied upon to tell the entire story reliably. The idea of “first and last,” (Alpha and Omega) appear in Revelation, as well, which ties that book to the Gospel.
Reliable witnesses in ancient times were those who knew or witnessed to the entirety of the sequence of important events. This is why the Word (from the Beginning to the End of all time) is to be trusted as the Alpha and Omega. Thus, John as a witness from the beginning to the end of Jesus’ life (first and last reference in the Gospel) is to be trusted as an authentic and reliable witness to the teaching and life of Jesus.
Bauckham also explains in great detail why some characters in the Gospels were named and others not. Much of this has to do with the year that each Gospel was written and how naming specific characters might have put them in jeopardy with the Jewish authorities.
So, for example, the woman who anointed Jesus in preparation for his entry into Jerusalem was not named in earlier written Gospels because that would have made her an accomplice as far as the charges against Jesus as “King of the Jews.” She anointed him in the manner that a king would have been. Also, making known the identity of the owner of the room where the Last Supper was held (the later meeting place of the disciples) would have placed him in danger. These characters could have been named later on when immanent danger to them had passed, say after the destruction of Jerusalem.
This is why John never names himself as the author of the Gospel, but places himself in it as a witness using literary and cryptic techniques. Partly to keep his own identity secret but also out of deference to the important figures in the Gospel story. He views himself as a very reliable witness but not an important character in the narrative itself.
If I recall correctly, Bauckham argues for an early dating of Mark, Matthew and John, but a slightly later dating for Luke. He makes a compelling case.