At-At from a military perspective is the fast way to pronounce it... "Imperial Walker" is simply a generic term that could apply to any number of pieces of armor on the field. It's a generic, "Holy **** I see armor!" kind of comment... It gets specific to the point of saying you see armor that's on legs, not hovering, tracked, or wheeled, but it's still generic.
A.T.A.T. is longer to say... Maybe more "official" but takes longer to say. It's likely military personnel wanting to identify walkers quickly would cut them down to "TE, ST, PT, OT, AA...", etc. to identify specific pieces of walker armor on the field with some speed.
The soldiers on Hoth that said, "Spotted IMperial Walkers" probably are identifying armored columns of some kind too... More than just AT-AT's. The films show of course AT-ST variants of course with the AT-AT's, and EU says other walkers were there but "off camera".
I'd say the "technical" name of an AT-AT is A-T-A-T, and the quick identifying name of them is At-At, just as AT-ST would likely be shortened to "ST" for speed's sake. And of course you can limit things to just "walker" or "armor", but that's highly generic and knowing what you're facing is obviously important for a variety of reasons.
And this is one dorky conversation. I love it. I should move this to the Classic Trilogy section I suppose, but... eh I'm tired.
Matt, "Chicken Walker" was used by ILM crew for the AT-ST's... Lucas used it too. It doesn't appear in EU that I'm aware of, and honestly I've never cared for the term myself as I don't think they really look like chickens and stuff, but I guess the ILM guys called them that all the time.