How was a common individual’s identity verified before the widespread use of identity documents? What was to stop someone from simply moving to a new area and changing their name in order to avoid debt repayment, punishment, etc?

I'm sure someone is going to give you a detailed answer to this question but I've come across it before and it's covered a bit in the FAQ.

This answer from u/naturalog (among others) in response to the question, "How were people identified prior to photography?" touches on some of the details I think you're after-- specifically what prevented someone from moving to a new area to avoid punishment for a crime.