Actually, by definition, you can call yourself a professional if it is what you do for a living. That is the difference in the show world as well, between someone who shows as a professional or someone who does A/O stuff.
But I think what you are asking is what kind of programs/ experience should you have to become a trainer?
I strongly suggest to anyone who is interested in being a professional -- become a working student! You will learn all aspects of riding/barn management/horse care, etc. and will get extra riding time/training that you otherwise wouldn't get. You also get to witness the head trainer you work for doing their job and discuss how and why they took a certain approach with a particular horse. You get experience with all types of horses as well, and generally have a broader range of knowledge than you would if you were to just take lessons and pay for training.
"The white horse moved like a dancer, which is not surprising: a horse is a beautiful animal, but it is perhaps most remarkable because it moves as if it always hears music."