When the Canterbury survivors are taken aboard the Donnager, they're identified via a scan of their neck implants.

Technological implanters are currently part of the Grinder community, and don't have anything as technologically advanced as this. At this point, it's a miracle if you're newfound implant isn't accompanied by a visit to the hospital. However, theres is no reason to think that implants haven't progressed far beyond this. In fact (SPOILER ALERT) we do see some implants in the next episode. What isn't clear here is whether or not Mars is scanning an impant or extracting DNA for analysis. Either way, both of these methods imply some sort of solar-system-spanning database of every person ever born. With a population of over 34 billion people this would be no easy task.