The G in GIR doesn't stand for anything while IR is short for Information Retrieval.
Explanation regarding this curious name:
GIR is created in the series' first episode, when Zim requests a SIR Unit (Standard issue Information Retrieval Unit)("it is also a thermos") from his leaders, the Almighty Tallest.
The Tallest, not wanting to give Zim a fully-functioning unit, offer him a new "advanced" model, which they claim they made just for him.
They then assemble a robot with parts from a garbage can, and put whatever they happen to have in their pockets into its head, including a paperclip and some change, instead of a brain.
Upon activation, the robot introduces itself as "GIR" then starts hitting itself. When asked what the "G" stands for, GIR جوابات "I don't know."
Other than the manifestation of personality in GIR, the only differences between GIR and regular SIR units are the unique coloration of the the luminous parts of GIR's body (teal instead of red) and his cross-hatched mouth.
In short; GIR himself has invented the name and even he doesn't know what it stands for.
I think the G should be for 'Garbage' but that's just me :)
Even though he never says, i think that Jhonen had it in mind to name him GIR making the G for Garbage. when spelled out it makes perfect sense Garbage-Issued Information Retrival Unit.
Well, Gir doesn't mean anything in particular. GIR doesn't make sense (Even though we all love him) so, it's possible that he just put three random letters together in some random letter, maybe it's because the Tallest put Garbage in his head, so instead of 'S', he put 'G'.