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One obvious answer is RFID tag microchip implants, for example attached to the ear at birth, at the same time as someone is given their personal credentials. The body can change but the chip will remain the same. This technology is already available today, used on pets and livestock etc.

There are of course many practical problems with this: is the encryption safe enough, data retention, will the tag need to be repeatedly replaced, what if someone cuts off their ear etc.

In addition to this tag, perhaps the "personal credential numbers" (social security number or whatever it is called in the specific nation) are only known to the person and the authorities, not the public.

To authenticate someone's identity, you could ask for the person's name, number, date of birth and the RFID chip itself.