The military uses ID tags with neck chains for a good reason. Take a look at what is on the DAN ID tag and imagine how helpful that information would be to you, if you were the doctor in the ER as the unconscious diver's body is rolled up to you.
I've personally been involved in several helocopter diver airlifts. My exerience is that the ONLY thing that goes with the unconscious diver to the hospital is what's on his body, as the diver is immediately cut out of his wet or dry suit (and no one ever goes thru the pockets). So, any kind of identification and medical information that is attached to the body is a thousand times better than something that is not attached to it. The DAN dog tags on a neck chain work for that reason.
Even conscious divers often may not have their witts about them, so they may be unable to talk intelligently to the emergency rescuers. I've seen that happen with one rescue where a trained air force pilot who was so confused that he had trouble remembering his own name. I showed up a couple of hours later and the hospital didn't have any of his medical data, his insurance numbers, etc.
Even if alert few of us have our medical information in our heads. I've even seen one rescue where the diver was cut out of his gear and even carried his wallet with him, only to have it lost before he got to the chamber in one hospital.
An ID around the neck is respected, left on the neck, and given top priority by rescue personnel - so it carries the message from the dives site, to the amublance, to the helocopter, to the gurney to the hospital, to the person processing the paperwork, thru the ER, to the chamber, etc. At least that's been my observation.
Sorry to say this, but having ID on the body also makes it easier for body ID for a found dead diver. I know that when I take a solo diving trip the first thing on my check off list is my neck ID tag for that reason. (I also leave my dive plan on my dashboard).
BTW: Most divers I know take a marker and print their names on their tanks. I also put a dab of red paint on every piece of gear I own so that when fins are in a pile on the dive boat, for example, mine stand out. Over time everyone I dive with know what's their's and what's mine.
If you are going to dive you have to look out for yourself, and a neck ID helps as it is helps those trying to help you.