My gamer tag is a reference to Samwise Gamgee from The Lord of the Rings. A friend got super drunk one night and called me "Dagamdagee." So that's more or less the long and short of it.
So yeah, just think of that "gee" part as in, "Gee, that sure is swell." That's basically how your pronounce my tag. See, wasn't that fun? I bet you're super happy you read this.