The only real "solution" would be to require all people, everywhere, or at least in the US, to get some sort of "personal ID marker" afixed to their body.....say on one's forehead or hand, where it would be easily located for unspection or use.
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Implanted chips might work. Some sort of barcode might work. But it would have to be permanent, non-removable, and not able to be used should it be cut from the person it belonged to. 
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That would, theoretically, make it an individualized and personalized marker that could be used for identification, prurchases, seeing you doctor, and every other way driver's licenses, credit cards, medical cards, library cards, and possibly even health club cards are used today.
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Two companies (one in Wisconsin and one in Sweden) are currently using such a RFID chip implanted in their employees who volunteer for it. It used as a "key" to open doors, access their work computers, and even buy snack items and food. 
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Oh, and it's coming.....in a few years.