I know there are quite a few places to buy them which you can probably find on the internet with a google search. Ebay would be a good place to look as well.
If you are interested in making your own for pretty cheap you could do one like this:
This is a stall plaque I made for my mare. I just used a pre-cut blank plaque which you can get at Walmart or Hobby Lobby for about $4 or $5. I spray painted it purple and added 2 vinyl decals (which I make) for the names. It has both her barn name, Lenore, and her registered name, Ten Talents.
If you want to make your own, here is an easy way to do it. (to make one that looks burnt into wood.)
Take a piece wood that your using as the plaque/name plate. Use a dremel to carve/engrave your horse's name into it. ( a small hand held dremel is pretty inexpensive)
Then take some black hobby paint (or a really good black marker) and paint inside the horse's name. Then take some dark wood stain (preferably the one that stains and seals in one) and cover the entire plaque/name plate. And viola! Your done...and it should look like you spent a fortune on it. :)