The others stated it.
Since I work my current ponies mostly in draft/work harness - I use the Draft Teamster words - haw - for left and Gee for right (there are actually a few other commands, too). However, I only use them when I want a sharper/tight turn (such as a pivot). I also use whoa, stand, step up, their name in front of a command, EZ, and voice commands for gaits - such as walk, ter-rot, can- ter. Since mine learn to lounge before they are ground driven, they also get sounds for gaits - cluck for trot and kiss for canter and I vary them in while driving as well. I have to think about it as I thought I was using a couple of other commands but I'm not remembering them right now. Also, I no longer use the haw/gee commands when I have a pleasure harness on mine - only when they are wearing a work harness. They know the difference. It's the same as switching from western to english riding - they learn a different way of carriage based on what they are "wearing".
If you go to a CDE competition you will hear all kinds of vocabulary and at an international event - different languages alltogether. Not every driver uses the same commands and some will use different commands while driving the dressage pattern vs what they use on the marathon course. Also some "purr" or "growl" - which means different things to different teams! It's really fun trying to figure out what some are asking their singles/teams to do!!
ADD - Forgot this - the Teamsters I visit with at various Plow Days also said you really should use only single syllable names for a "working" horse. Makes it much easier to call them by name when working more than one at a time. AND don't make the mistake of naming one similar to the commands you will eventually be using. "GG"s name can be confusing when prefaced before the command "Gee",
. I didn't know this before the barn name "stuck"... So I usually start with GG, then say Bell (her dam and current driving partner) - Gee.
Pic of Bell (left) and GG (rite)
and it's really wild hearing the teamster calling all of these horses by name!!