Not sure if you’re asking for brand names or more specifics.
I use a laser cutter at my local community college’s Fab Lab to etch mine. Theirs is an Epilog Mini (50 watts, I think) and has a 12" x 24" bed.
(Btw, ‘Fab’ here refers to fabrication.)
There are a lot of different kinds of laser cutters out there, so be sure you are getting one that will do what you want as well as one you are comfortable using.
A lot of the less expensive ones require a lot of geekery to get working, from coding skills to using a (literal) bucket of water to cool them.
My recommendation would be to first see if there’s a Fab Lab in your area where you can pay a fee to use their equipment (not only laser cutters, but 3-D printers, CNC routers, etc.).
You might also want to see if you have a community college in your area that has what you’d like to use. For instance, my local one not only offers classes in Digital Fabrication (which includes laser cutters) which I love, but also is now offering an Open Lab through their extension program. Anyone can sign up for that, as far as I’m aware.
It all depends on where you live, of course.
No matter what your solution, it does take a lot of experimentation and trial and error to get good results. Paper stock, laser power, etc., all factor in, and you’ll still need a bit of geekery when learning how to create your image files so your laser cutter will know what to do.
If you only need a few paper dies made, you can always go through the Etsy shops that offer custom work.
Hope this helps you. Sorry I couldn’t give you a list of brand names.