Although, I will say this: I don't think people should be able to make the current models on the market. I think players should make their own brooms entirely. It would be more accurate to make broomsticks very customisable. There would be the different parts that would be sold in shops, the quality of those would determine the price at which they're sold. Obviously then, which parts are used to construct the broom will affect how it works before it's bewitched. It would be cool if players could have the option to construct it without pedals, but if they did, it would make their broom generally harder to control, never being fully smooth while flying, but broom level would count (like before the times of racing broomsticks, built for better speed and control).
Then you would have the magical portion, I mean, how I see it is that you'd have the general spell that bewitches a broomstick to make it a flying broomstick, that would make the broom perform based solely on the parts used to make it. Then, for higher level customisation, you would have other spells that would affect it, such as the Braking Charm, which makes brooms stop more precisely. There could be other spells that affect how fast it will be able to fly and maybe even others spell, but yeah, that's how I see this whole thing working to me.
In the end, they can name it whatever they please and it will be their personal model to do with as they please.