Second letter in his name is A, as his name his Jane Doe according to canon.
Although that's true, Jane Doe is a name used for a female whose name is unknown
So his name could still be unknown
And while on the topic of the Soldier, perhaps he himself was the one that chose to be titled as such because he's obsessed with trying to be like a real soldier whose had a rough life and thinks he knows all about being in the military, Sun Tzu, The Art of War, and so on
I think that would actually make sense seeing as his alias is
Jane Doe and not
John Doe, Soldier's not a very smart person, especially when it comes to actual military stuff, which shows just how unintelligent and how much of a crazy person he is
I know there's all the comics and such that also show the Soldier being a complete moron, but i'm referring more toward game related material like Meet the Soldier and the Soldier's bio on the TF2 website