I can't answer in general, but I've noted something that appears to be true of antebellum America (roughly 1800-1860), that can partially answer how people were identified. In Joaquin Murrieta by John Rollin Ridge (a fictional novel, meant to sound like a biography I'd say) the characters identify themselves to others through letters. In one case, Murrieta has to save a compatriot and poses as someone else to do so. He "proves" his identity (to give his compatriot an alibi for a crime) by presenting numerous letters addressed to him, marked with the stamps of post offices around the nation.

Similarly, when attempting to verify the story of Solomon Northup (Twelve Years A Slave, book not movie), letters and the testimony of those who knew him were used. His story was validated by letters and other testimonies (this was pretty difficult, slave narratives were widely attacked on credibility claims), and when he was found by his friends from the North and freed, they showed numerous letters to prove both who they were, and that they were there for him (and obviously established in good faith that he was who they said he was).

That might be of interest, as far as identity verification. I distinctly remember this question coming up before, but I'm on mobile, so I'd suggest searching the sub :).

Edit: Found the thread from two weeks ago :). Enjoy!