A hearing dog is a type of assistance dog specifically selected and trained to assist people who are deaf or hard of hearing by alerting their handler to important sounds, such as doorbells, smoke alarms, ringing telephones, or alarm clocks.
After passing initial screenings, they are trained in basic obedience and exposed to things they will face in public areas, such as elevators, shopping carts, and different types of people.
Generally, training involves getting the dog to recognize a particular sound and then physically alert or lead their handler to the source.
Incidentally, in the United States, a hearing, signal, guide, or any other service dog is not legally required to have or wear any badge, leash, collar, or any other identifying item.
They wear a bright orange leash, collar, and harness to identify them, and carry with them an issued ID.