Sorry; the speculations on things Johannine are becoming progressively wilder as it gets late and I am more and more carried away. If I am a bit late with the P.P.S. idea about the Gospel of John's original ending, I'll bet no-one has thought of this one... [Oh, yes they have, as I have discovered. Martha has been under suspicion for the address of II John: see below.]
There is a dispute about Eusebius, Papias, and the authorship of the second and third Johannine epistles, as well as the book of Revelation. Eusebius seems to quote Papias as saying that he heard eye-witness accounts of Jesus from the Lord's disciple, the Elder, πρεσβύτερος John. He is called (by Papias, whose life may have overlapped with John's by up to 30 years) a "surviving" witness. He has however, named John, along with James and so on, in the sentence before, as being the Lord's disciples. So it seems that he is either repeating himself (because John falls into two categories, both a group of Apostolic witnesses, and also a smaller group of living eyewitnesses), or he is (Eusebius thinks) talking about two different Johns: John the Apostle and John the Elder. I am inclined to agree with some commentators that Eusebius is fishing around for an excuse to deny Apostolic authorship of the book of Revelation, which he doesn't know what to do with, and which he wants to offload onto a putative second John, the Elder. Eusebius really didn't like chiliastic beliefs and Revelation 20 was always going to be a problem for him. The difficulty with this theory of Eusebius is that he is the only person to even mention the existence of two Johns; what little else we possess of Papias and every other Asian author in the period of the Apostolic Fathers points towards a single John at Ephesus, the Apostle.
The epithet "the Elder" is present in Peter's writings too (cf. I Peter 5) and seems in Peter's epistle to identify Apostles and the most senior of the Christians, and to be contrasted with the νεώτεροι, or "young" in the faith. One of the problems with interpreting words at a distance is that they can be both "official" - in the sense that presbyter was a term for the assistant of the episcopal president at the Eucharist - and also "everyday" language: the word presbyter in Peter is possibly designating the original disciples of Christ, who are the Elder in the faith, as opposed to the "young" who have been baptised by them. So designating the Apostle John as the Elder is entirely consonant with him being the Apostle; and the same goes for the Apostolic authorship of the second and third of the Johannine letters.
Now for the theory, on II John. What is the rather cryptic absence of names about? A need for secrecy, so that an intercepted letter would not incriminate? There seems to be more to it than that. The letter starts with an address to the "elect lady" who is referred to as beloved of all those who walk in truth, where Truth is being used as a name of Christ. Why is there such a general presumption of love for the elect lady from all Christians? The epistle is to the elect lady and "her children"; but it becomes clear later on that her children are in fact the church to whom John is writing, who must keep out the Docetist heresy. What church was under the patronage of a lady - if this was a church meeting in her household merely would they be called her children, especially if they are later addressed as being responsible for giving heresy short shrift? There is also an abrupt change of address from singular you to plural you at two points in the letter - John reminds the lady (singular) that the lady heard Christ's commandment of love "from the beginning", that we (John and the lady?) should love one another, before going to extend the command to you (plural), presumably to include the lady's children. The plural you is then continued to command the exclusion of Docetists. He then signs off with a personal greeting to the lady, from the children of the elect sister: again, some kind of spiritual maternity is being spoken of.
I think that the letter's contents, and especially the introduction to the lady who will (John is sure) be beloved of all Christians, point towards a lady who is significant in the story of the Gospel, and who would be known by all. The options are rather few: Mary, Martha, Mary Magdalene... Mary the Mother of Jesus?