@Kaled: I tend to work on a principle of "You know what the character knows", be that set out in their original backstory, or something the GM has told you before the game. Unless No-Name's armour causes some kind of amnesia, I think we can agree the character at least knows who they were.
I'm of the opinion that a character not having a backstory set down on the basis that they "never tell anyone their history" is pretty dull (and in quite a few cases, outright lazy).
So my backgrounds cover what the character knows, what others may happen to know (be it true or not), and possibly even things the character themself doesn't know (be it about them or their equipment).
... Okay, there are a couple of cases where I've explicitly set out there's something that some of my characters know, and which I don't - the reason being that the information in question is beyond the human mind's capacity to imagine it, and instead it has to be told/find it out. And in those cases, it would be pretty daft if I knew said information.
It is a matter of personal taste, I know. But I just don't allow myself to use any "short-cuts" like that in writing character background.