Sometimes the defensive check is predetermined based on what the offense is doing, so they may call out a formation change (1-back, trips, fullhouse) and everyone on the defense knows what to do.
If they decide to call out an adjustment, they're going to probably be a little more cryptic. I coached a team that played quarter-quarter-half coverage, but we never said all that. It was just called bandit. Formation to the boundry may require us to have more of traditional Cover 3, so we called Squeeze.
Names can become common, so if the defensive lineman start yelling "twist" the offense will probably figure it out.
In the huddle, it is typical to have this format:
- Stunt (optional)
- Key/Tag (optional word that may be a slight variation).
So - Tight (shift line to TE), X (twist stunt), Cover 2 , Sink (tag for LB to drop deeper than normal).