The man in blue will supply "You" with a clip of ammo after each visit and can be seen as a last resort to get more ammunition.
The man in blue often exhibits an aggresive demeanor, and seems to stand in direct polarity to the "Man Who Wears a Box". This is displayed overtly in their different behaviors, and subtly by the fact that they provide two very different items: While the man in blue provides ammo for your handgun, which in turn promotes a violent and destructive playstyle, the "Man Who Wears a Box" provides batteries and food, which promotes a peaceful and pacifist playstyle.
According to Jasper Byrne, one interpretation of the man in blue is that the he represents the "Nature" part of the Nature VS Nurture debate. In that sense, the man in blue would represent that "You" is inherently violent and that his innate nature may override his choices and environment.
It is likely The Man in Blue is called 'Draco', as many notes that talk about killing the Monsters and violence are signed off by a man named 'Draco'