As far as I know, you can't get that information directly
A strange and roundabout "hack" would be to get the string of
the user's documents folder or desktop using
"air.File.desktopDirectory" or "air.File.documentsDirectory" and
parse it to get the user's name.
This is, of course, VERY unreliable, but may be the only way
to get the currently logged in user's name.