The go-to source for these kinds of questions is The Return of Martin Guerre. The story occurs in the mid-1500s, so it's at the outer edge of the Late Medieval period. Still, it could tell us something about older practices.

In this story, a man named Martin Guerre went off to war. Eight years later, an entirely different man returned, claiming to be Martin Guerre. For three years, the fake Martin lived in the village the true Martin had grown up in. He inherited property from Martin's father, and hadn't child with Martin's wife. Increasingly, however, fake-Martin's identity became suspect, particularly as he got dragged into a fight with other members of the Guerre family over some inherited land. Eventually, the patriarch of the Guerre clan sued fake-Martin for being fake.

At the ensuing trial, fake-Martin was interrogated about details of Martin's life story and his relationship with his wife. Other villagers were called to testify against the imposter. When the real Guerre appeared, the imposter was hanged.

So, what does this tell us? In short, one's identity, when push came to shove, is something defined by other people. Proof of identity was sought through a person's ability to retell intimate and personal information. The person verifying a person's answer would hopefully themselves be trustworthy.

The takeaway is that, in pre-modern times, much of the world ran on face-to-face personal connections, and there was no way for a government to track and manage every subject.