Just a few off the top of my head...
GAR-15
(pronounced gar [like the fish] fifteen)
Gi15-H
(Like the longer barreled MK16)
Gi Mediator
Gi "bigger stick"
G15 combat blowback "The Machine"
Gi-Gun
Gi2010-15
(To keep the military tradition of naming guns after their year)
Gi15 Exterminator
Gi15 Diplomat
I think that "GAR" would make a great series name because it makes it obvious it's in the g4 line, plays on the AR series name, and is associated with a predator that's both fast and deadly. Not to mention that Gar sounds cool.