If they don't have documentation, are they citizens?
Yes. As OP said, "anyone who has changed their name and does not have a notarized copy of the name change certificate, and most people who do not drive." Note that the first category includes many married women.
This is part of the US constitution. There's no "if they have proper documentation" qualification.
An executive agency creating new requirements for citizenship has the effect of overriding the Constitution, which brings into question what are the controlling documents for the country.