PSacramento.....The book is technically anonymous; the title is secondary to the text, which nowhere names the author. However since ch. 21 was written by a different author from the main body of the text (cf. the original ending at 20:30-31, and compare with 21:25 which echoes it, and especially cf. 21:24 which comments on what the beloved disciple wrote down: "we know that histestimony is true"), it is likely that a "John" was responsible for the book's final form, whether John of Patmos or John of Ephesus (it is unclear whether they were the same person), much less the traditional John son of Zebedee who did not live into the 90s but died fairly early according to Papias and other (Eastern) traditions that run counter to the more popular traditions in the Western Church. As you may know, Papias (who personally knew the latter) distinguished between the apostle John and John the "elder" (= John of Ephesus), a title that appears in the letters of 2-3 John (cf. Jerome who assigns 1 John to a different author than 2-3 John), and the statement in 21:24 is in fact echoed in 3 John 12 ("you know that our testimony is true"). So the title may come from the name of the person who put the book into its final form.
why not simply mention that Lazarus is the one he loved? Do you think there was a particualr reason for this? maybe because Lazarus wasn't one of the "12" ?
As I mentioned above, it may be for the same reason why Paul is very coy and indirect (by referring to himself in the third person) in relating his visionary experience in ch. 12 of 2 Corinthians — modesty. Before he broke down and related his experience, Paul ranted at length against the sin of boasting. If the author wanted to make an authorial claim of being the same person as the beloved disciple, being indirect may be the best way to do so if he also wanted to claim that the beloved disciple was more privileged and important (e.g. specifically loved by Jesus, reclined upon by Jesus, who remained at the cross when the Twelve fled, who reached the tomb ahead of Peter, who "saw and believed", etc.) than the other disciples.