I have a theory for who he is, but it's a bit extensive, so I'll just say the basic parts. G-Man is a term used in the US government, it means government man. With this in mind, I thought he might be an interdimensional bureaucrat/ representative for an interdimensional government. This interdimensional government would be at war with the combine, due to the combine's hostile actions against multiple alternate universes and dimensions. The G-Man was tasked with getting the combine on earth so that humans could deal a crippling blow to them, helping their war effort.