I get questions all the time about exactly what to say to your driving pony. It can be confusing to know what exactly to say.
First, most natural horsemanship instructors will tell you not to talk to your pony. They can't understand human words/language and only listen to the tone of voice. So therefor one should not use voice commands. Through my own horsemanship studies, I understand that they want us to focus more on our body language than on voice commands, this is far more for the human than the horse. There certainly is a time and a place for this!
On the other hand, I have also been around people who never STOP talking to their horse, "oh sweetie, you're so cute! goooood boy, so handsome and smart and wonderful. Mommy thinks you are the cutest...." and on and on. This is NOT what I'm talking about when I say Talking to Your Driving Pony. And if you do this, please stop doing it. LOL! There is such as a thing as too much talking to your pony. Too much talk will take the power away from the words they can learn and respond to. Watering down the commands that we actually need!
I rarely talk to Zorro when we are driving. Sometimes if he is nervous then I will quietly talk a stream of pretty much nonsense, mostly for my own benefit! But mostly I rarely say anything to him unless I am asking him to change gait. "Zorro, trot! Zorro, walk. Zorro, canter! Zorro, whoa." And yes I always say his name before I tell him what I need him to do. I, personally, don't use directional words, but understand why people do.
If you want to teach your driving pony directional cues then I suggest using Gee (right) and Haw (left). These are the universal words for these directions. If you ever have to sell your driving pony he has a better chance of succeeding if he is using universal language.
As for the idea that horses can't learn words, I say nonsense! Zorro knows quite a few words and he knows what to do when he hears them. Sky definitely knows the word "NO!" LOL! So no one would ever convince me that they understand any less than dogs do!