Remember Casino Royale? Not that one, the good one with Woody Allen and David Niven.
Growing his brand for one punk slumdog in the post apocalypse cursed Earth wastelands would be hard... And really! All your eggs in one basket? What sort of greased fool still does that?
In Casino Royal, MI9, whoever, realized that when the badguys figured out that it was THE James Bond who was on their six, that it was brown underpants time and they might as well surrender immediately, which is what they inevitably did. Brand recognition. So Military intelligence decided then and there to legally change the names of all their other secret agents also to "James Bond" so that Her Majesty's Secret Service could win every battle on every front without firing a shot.
Are we positive that there was only one John Conner?
Are we positive that the "real" John Connor made it to the head of the Resistance?
(Sarah could have made hundreds of copies of that Photo for John to pass on/out to whoever in the hopes that it would make it's way to either Kyle or Skynet... Oh my... Just like in Fight Club too.)