Reichu: Yeah, I've wondered that myself. The only dictionary definition for "pallet" I can find that even goes near the domain we're talking about is this:
A projection on a machine part, such as a pawl for controlling the motion of a ratchet wheel in a watch escapement, that engages the teeth of a ratchet wheel to convert reciprocating motion to rotary motion or vice versa.
Uhhhh… That's real helpful. There's got to be SOME sort of reason for the name. Or maybe these Eva weapons are just supposed to have generally incomprehensible names, so long as they "sound cool". (To a Japanese audience, anyhow.)
Hexon.Arq: I would think you could call it something much cooler than "Pallet Gun". It makes it sound like a daffodil-shaped contraption that fires ping-pong balls.
HeWhoPostsStuff: Maybe it's pseudo-Engrish for "pellet?" Still doesn't sound particularly threatening though… which make it rather appropriate since the weapon turns out to be all but useless, heh.
Reichu: "Useless" on all but the poorest excuse for an Angel, ol' #09 in episode #11.