Why could the Connors not just pick another alias?

Question

In Terminator 1, during Reese's questioning, the following dialog takes place:

Doctor - Why did terminator kill the other two women?
Reese - all the papers and archives were destroyed during the nuclear war. Skynet did not know anything about the mother of John Connor, it did not even have a photo of her. It only knew the name and the city. So terminator acted like any machine - systematically.

And this brings the logical and the biggest question of all time. Why could John Connor not simply change his name after the war with Skynet broke out? In that way, Skynet would never be able to trace him or his mother in the past.

Answer 1

He knew from his mother's tapes that the terminator had to go back in time and that he had to send Kyle Reese after him else he would not have been born and the war would have been lost as he would not have been there to lead the humans in their escape and war.

I cannot recall the dialog exactly but Reese mentions to Sarah that "[humans] were that close to going out forever" and then "there was one man who taught us to fight, to storm the wire of the camps, to smash those ... into junk".

Clearly John Connor was a unique individual who was in the right place at the right time. If he had never been born the odds of a similar person being in the right place at the right time in the time humans had left is very low.

Answer 2

In universe answer:

A lot of cameras have recorded the face of John Connor (even John Connor + badass mother), so his face must be in several hard disks and SkyNet is supposed to have control of everything digital wise, so I guess, when SkyNet rise to power it recovered images of John Connor, and then just run some recognition software and that's it!.

If facebook can tag people automatically so does SkyNet.

Answer 3

I am not familiar enough with the stories to know when time travel was invented — and by whom (or what!) — but… the move would only work if he made it very soon after the war broke out… and the concept would only work if time travel had already been invented at that point. (He has to have the idea, and put it into effect with (effectively) every human being who might hear of him as the leader of the resistance, before SkyNet first hears his name (as the name of the leader of the resistance).)

(If it was my life, in the real world, I would have the idea about five minutes after it was too late.)