Anything from a single point punch to a small circle punch to a small flat punch with a grid of teeth cut into it does good work.
The single point punch is slow and can end up punching too deep especially in softer wood.
A small circle punch is often used and a common nail set is the tool used.
Sometimes used as-is. More often it is carefully sharpened to better define the outer circumference. That leaves a better pattern in the wood when struck. It's somewhat blunt especially when compared to a single point tool so it puts down a nice surface w/o punching a lot of deep holes.
Makings a tool just for matting a surface is common in the engraving trade. It's just a smaller version of such tools used in the leather tooling and wood carving trades to do the same effect in background work.
Lay down a matted surface, do it fairly quickly and evenly.
For a wood working tool,,no need to harden the tool really.
Take a 1/4" sq or rd piece of steel and file a pattern into one end/face of it.
Criss=cross at 90* lines to one another like a checkering pattern. Micro fine is not needed. Keep them as even as possible.
You can cut the length off to suit you as a punch and use it to matte the wood surface striking it lightly w/a hammer.
It covers fast even in a 1/4" size.
Make one with a square or narrow edge to fit into corners if doing work inside borders. You can work right up to the edge that way.
Vary the surface texture of the punch for different effects.
Make them smaller and harden them and they become metal stippling punches. There you can put the texture in the face with a liner graver and it works very well. Tiny circle punches were made when you needed them by hollow cutting the tip of a piece of drill rod w/a flat graver and then sharpening the point down around it and harden it.
I still make them that way.
The punches are available now quite inexpensively for sale. I just like to still make the things.
They used to have a bench block called an engravers dapping block you could buy. You simply hammered the punch blank into the appropriate size hole (of many) in the block and the small inset formed the circle punch face. Then you sharpened and hardened it.
Old school,, and it was too expensive..
