They were like newborn infants. They could not walk on their own the moment they were born, but many months later they would finally be ready.
Furthermore, there were more concrete reasons to be secretive about this fact.
If finding a true name for one's Martial Art was a measure of how uniquely original one's Martial Art was, which would in turn indicated how cognitively boosted your brain was, then the young brash fools would hastily name their Martial Art in the hopes that this was a sign they had made a lot of progress!
They would be putting the cart before the horse.
If naming one's Martial Art was a profound and important act, and it certainly was, then young hasty and greedy Martial Apprentices would certainly screw things up for themselves.