I guess this question is more like can I use a single word as the default AD user group for users (currently it is "AD\Domain Users").
If I can, I would like to use something like "users" or similar. How could I do that?
What problem are you trying to solve with this? As Ryan points out, so succinctly, this is not a good idea at all.
I can't think of a single case where there would be a benefit to changing this name, so instead of messing with a well-known built-in group for no reason, you should just leave it be.