The name G-Man is never brought up in any of the Half-Life games, it was merely pulled from the files of HL1 as that was what Valve named the model file of him, and became what the fans use to refer to him. It is presumably short for "government man" and is an old American term I believe.
Anyways this isn't a new theory, I've heard it plenty of times before and its a pretty flimsy one... Sorry to burst your bubble though OP.
HT_Black said:
The G-man is really Gordon's intuition as manifested in his mind. Want proof? Count how many times you see him in Half-life2 just before encountering either a new type of enemy or a set-piece. Seriously-- count.
Interesting, but this can't be right, otherwise other characters wouldn't be able to have any contact with him. In Episode 2 he clearly comes in contact with Alyx who ends up delivering a message from him to Eli, and due to what Eli tells you afterward its obvious Eli is aware of his existence and has had contact with him in the past. Also, it's quite obvious the Vortigaunts know about him, as they stop him with a force-field at the start of Ep1.
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What interests me the most though, is since way back in HL2 the vortigaunts have obviously been in contact with the G-Man in some form. There are plenty of occasions where the Vortigaunts make references to him in HL2, + Ep1 and Ep2 I think (though to be fair they are all quite cryptic).
"We serve the same mystery."
"Something secret steers us both... We shall not name it."
"Far distant eyes look out through yours" < but to be honest this could either be a reference to the G-Man watching Gordon's every move or a fourth-wall-breaking joke about the games First-Person viewpoint
There are some more, subtler ones which are debatable, but those are the best ones.
Also, near the start of HL2 a little while after the action begins, you drop down into a train cart and the Vortigaunt and a civilian are watching the small TV, and if you look closely in the split second before the Vort hastily turns it off, you can clearly see the G-Man on the television presumably giving a message to them.
The G-Man is definitely using the Vorts in a similar way to how he uses Gordon, in my opinion.