I've never seen this, but hunters in our area that use hounds usually brand their animals, as well as tattooing.
It can be useful if your animal is particularly far-ranging (so if you are hogging or going after big cats, usually). And there are areas of the country where the theft of good hunting dogs is far from uncommon. It allows easy, immediate recognition by the owner of the dog.
Unfortunately there are a lot of issues with dog hunting, and there are certainly hunters that see their animals only as producers. A dog that doesn't perform will often be culled or abandoned (or pawned off on another less experienced hunter).
Obviously this isn't true for all hunters: my family hunts recreationally with our dogs, but they are first and foremost considered pets. An animal that doesn't produce will be retired to long runs in the woods and a lot of couch time =)