Usually the reason why magic is split up into schools while Martial arts usually isn't is mostly because "Magic" is so vast a subject that it could basically be "Science". It is a list of vastly different ideas, concepts, and abilities put into one thing.
While martial arts may have aggregate skills, they are all about the exact same thing.
If you are making ability names for your martial arts you need to think about how exactly you want to split them up.
One thing you can do is just make them up entirely
As for Axes and Maces: Berserking
It gets the general idea (Hitting things HARD!) and allows flavor at the same time for what it could do.