Yup. Nearly every facility capable of transfusing a patient will run a test on the blood type before giving it.
But, wait. How would they guess it was your own name? It could be your
ex-lover/murderer, for all they know. If you were a CSI and you saw:
Tom Cruise
666-66-6666
AB neg
Scientology
tattooed on a headless body, would you assume it was, indeed, Tommy Imustcontrolall Cruise?
Besides, I should have added fingerprints, when I said DNA.
(Disclaimer: I don’t really know if Tom Cruise’s blood type is AB neg, or if his SS# is the number of the beast.)
Shhhhhhhhh… we don’t want this, or the fact that being an AB+ I can receive blood from all donor groups, to get out to the population of less knowledgable, easily impressed 18-24 year old females. 
Name I get, also social security number and blood type. But why would someone need to know your religion?
So they know the burial custom/ceremony you prefer.
In case you happen to find yourself at the hands of the Spanish Inquisition. Wouldn’t want them getting the wrong idea.
If the head is gone, it’s a little late to worry about a blood transfusion.
Bingo. I prefer to have all my bases covered–whether I be conscious, unconscious, or on another plane of existence. 
Tripler
I mean, if you’re gonna get inked, might as well make it useful, eh!
Flipping through a back issue of Rolling Stone, I found and article about a troop of Marines where one guy had “Tag goes here—>” on the arch of his left foot, pointing at his toe.
Hard core.
I can’t find a picture of it (google has failed, alas!), but someone in this universe has a full color, full back tattoo of Pooh crucified. Alas, google, thy fickle links!
Nearly?
Who doesn’t? Please tell me so I can avoid those places! Or, at least, offer them my services as a blood bank tech. 
I gotta ask: how long does just such a test take? I don’t want the nurses taking half an hour to type my blood if I’ve got a sucking chest wound *. I might as well give them the information (or at least a clue) up front.
Tripler
*Why is it called a “sucking” chest wound? Because a chest wound usually sucks.
My understanding is that under the circumstances you describe they can give you O Negative until they determine your proper blood type.
Still, if that’s the case what’s the point of putting the blood type on your dog tags (among other places)?
Seconds. I’ve seen paper strips like the ones used for pH testing, you just dip it (or drop a drop onto the strip), let it dry and compare the result with a chart.
Many people think that “machine” results (which take longer, and of course fancier equipment) are better; the lab manager at the local hospital has done a lot of work in the field of comparative analysis (measuring the same thing by several methods to determine which methods give equivalent results) and a well-prepared paper strip is as good as any machine. Plus, they’re a lot more portable and don’t need batteries.
I so, so wanted these to be true, but it turns out it’s a satire newspaper.
http://www.soufoaklin.com/tattooartist.html
And the follow-up article, with the artist continuing the fun while in prison:
I worked with a bunch of Navy divers a while back. One of them had a bunch of scars on his torso. When asked what they were from, he replied that he had all his dog tag info tattooed there but had to remove it for security reasons when he went into “another line of work”.
This is something I have been railing about for years! I do not understand the attraction of getting Chinese symbols tattooed on American bodies. That is, bodies of Americans who don’t speak Chinese. What exactly is the point? “This says I am a beautiful goddess,” she might enthuse. Well, so what? To most of the people (yourself included) it looks like artfully arranged sticks. There is no meaning.
I do like the toe-tag one, though. Now there’s meaning.
About 15 years ago, a female friend of mine got one of those tattoos. She choose the Chinese symbol for “life”.
She was really happy with it until she showed it to a Chinese friend of hers.
He looked at it, gave her a quizzical look and said, “Why did you get “Moo Shu Pork” tattooed on you?”
She was pretty upset until he admitted he was joking.
Hmmm. I wasn’t expecting that.
But seriously,
Well, if you find a body (headless or otherwise) with the name Joe Johnson* tattooed on it, you’re probably going to try and contact Joe Johnson, whether he is the deceased (in which case you have a missing person connected to the body and can start some testing) or just a friend of the deceased (in which case you have someone who may know the deceased and can help ID them.) Either way it would help.
*Disclaimer: The name Joe Johnson was pulled out of thin air. If it is yours, you may claim it at the Lost and Found desk.
Unless something has changed, in the military the “tag” as in dogtag, goes between the front teeth. In case you didn’t know, that’s what the dogtags are for. ( I was an Air Force medic before I went to nursing school.)