As far as I can tell, it is jsut refered to as “a medal of honor.” It’s not like a Rebellion has a long-standing tradition of medals and awards for valor. They probably just spray-painted a couple of coffee can lids gold and hung them from a few pieces of colored plastic that were wrapped around the last shipment of soy-burgers.
They weren’t medals, they were the barettes Leia used to make the double side bun hairdo that she never wore again. Chewie didn’t get one because Leia wasn’t interested in doing him.
The “official” reason is that Chewie owed Han a “life-debt” and therefore anything he did, he did for Han, not for reward. The real reason is that Carrie Fisher was too short to reach over Peter Mayhew’s head with the ribbon!