I have not found anything about the real-life origin of the term AT-AT, but even if they were not named in the script, they were named by the time the 1981 Kenner toy line came out.
From the in-package catalog:
Imagine you're DARTH VADER with your giant 17½" tall, 22" long AT-AT.
Legs can be posed and a lever moves head in any direction and also
makes the two laser cannons light up and pulsate. Two Action Figures
fit in the AT-AT's head. Two laser guns turn with a clicking sound.
Remove side door and the AT-AT can hold up to 10 Action Figures. Two
"C" batteries not included. Assembly required. Available Summer 1981.
Since I could not find any factual origin information, here are some speculative reasons:
By the time Empire was released, GL and team were writing the script
for Jedi and they added different kinds of walkers to that movie.
Now they needed a term to differentiate the different kinds of
Star Wars is heavily connected to merchandise. Since they have a toy based on everything from the movie, marketing might push them to come up with a Star Wars type name for everything in the movie.