G.
That's all he'd ever known himself as.
G Callen. Nobody had ever told him what the G was for, and while a part of him wanted to just make it into 'Greg' or 'Gavin' or some other 'G' name, a much bigger, more influential part kept him from doing so. G was simply a letter in the alphabet, nothing special. Even Jason's attempts to make his name cooler (G-Force, G-Money, G-Man were a few examples) had not kept the odd looks that he had received – and still does- when he introduced himself as simply 'G'.
But it was all he had, and he didn't plan on just throwing it away. Whenever he went undercover, used an alias, he always looked forward to the end when Sam would come up, pat him on the shoulder, and say with a tone that he assumed a brother would use, "Good job, G."
As Shakespeare had once said, "What's in a name? That which we call a rose by any other name would smell as sweet."
And, hey, G was better than being named P.