I would imagine the reason Probate was granted in the name of Stirling Cameron would be because the Will was written in that name. If that was the name he generally used, then it wouldn't be a case of it being the "wrong" name - you can legally call yourself anything you wish.
As for why it took so long - all sorts of reasons. Maybe his widow just did not know there was a Will, and only discovered some years later, or maybe, being illiterate as you say, she just never bothered with it until it was needed to release some asset or other at a later date.
Or maybe, with the death being registered in his birth name, it took a while to verify that this Will really did belong to the same person.