Ex-USA readers, where are you, and how does your country handle this?
Countries without voter ID requirements for elections at the national level are short: Australia and New Zealand. Close is Scotland, which does not require photo ID for Scottish government and council elections.
In the US, some states require voter ID to vote in national elections, while others don't.
So the US, Australia, and New Zealand are outliers.
It really boggles the mind why it is such a contentious issue in the US.
If you for some reason can't provide valid ID, but the one collecting your vote knows you, that person can vouch for your identity[2]. For example if you're an inmate, one of the prison guards can vouch for you.
[1]: https://valgmedarbeiderportalen.valg.no/ofte-stilte-sporsmal...
[2]: https://lovdata.no/nav/lov/2023-06-16-62/kap6/%C2%A76-11
Until then, if you voted early and gave somebody else's name, you could have voted twice.
I don't think this happens often. It would have been included in the report of possible irregularities that is published after each election. I looked through the reports after two or three elections, and never saw reports about this.