You're right, "canter" does sound a lot like "Banner."
Still, you could use the word if you had a very specific intonation for it. I taught all my voice commands on the lungeline and then transferred them over to driving so Kody goes by the same two syllable "Kody, Ta-Rot!" and three syllable rising "Kody, Ce-An-Ter!" that my riding horses have all lunged to. It's important that you don't let them fall into a canter from a fast trot but rather collect them up, half-halt, then give the clear voice command and lift them into the faster gait. If you let them fall into it not only will it be ugly and hard for the horse but they will start to break when pressed for speed at the trot. (Not that they won't try anyway, but you'll have a clear standard for them.)
Before you try it in harness your horse must thoroughly understand the voice command on the lunge or in the roundpen and do it without resistance (no hollowing the back or throwing up the head). Then the first time you try it make sure you set him up for success. Do it on a hillside or in a big field, somewhere he wants to break anyway. Let him transition naturally and keep everything calm and happy, then ask him to return to a trot and praise him when he does. Kody's first canter was entirely accidental- we were tailing a pickup truck full of people from hazard to hazard at a clinic at Happ's our first season and he broke into a canter to go faster. He seemed a little hesitant at first waiting to see if I would pull him back or punish him and when I didn't he settled happily into it and off he went, nose-to-tailgate. I was waiting to be yelled at thinking I had broken some unwritten rule of driving but when we got to the next stop all I got was congratulations and mild admiration that my green horse was already cantering so well.
Green horses are going to want to rush forward into a canter, that's all there is to it. It's hard work to teach them to transition nicely without a leg or seat aid to help! Kody and I are working on that this year as it is time for him to learn to do it in an arena and to begin to learn lead control. I keep wanting to push him into it and must remind myself that if he doesn't do it in the first three strides I need to collect him up and try again. The first time he succeeds on voice command, don't worry if he falls out of it a stride or so later. The horse must build muscle before he'll be able to hold a canter in harness and especially on a circle or turn. Praise him heavily for doing what you asked then don't rush to do it again! Let him think about it while you go back to trot work and other normal stuff. Once is enough for the first time. The more you make it a nonchalant, not-a-big-deal thing, the less they'll be inclined to break on their own or go crazy for speed.
Other cues tend to develop by accident along the way. When I need my gelding to gear up for a tough pull uphill or through deep sand I say "Kody, hup! Hup!" once he's already cantering and he knows he needs to lunge hard. When we're approaching hazards I ask "Kody, are you ready?" His ears always flick and he gathers himself, then as we hit the ingate I say "Okay Kody, let's go!" and he cuts loose at a gallop. I've worked very hard this year to establish that if I haven't said "Let's go"...he'd better not! *LOL*
Good luck and I think Banner is doing very well. What program are you using to create all these inspirational poster images?
Leia