"Again, the civil code says the person making the acknowledgment must be the person NAMED in the document."
Agreed.
"Those four sets of names above can be all the same person but are four different people *when notarizing* because a DMV will only issue ONE license in ONE set of names, so Jane is ONE of those persons above *when notarizing*."
Here I kind of disagree, but maybe it's just a question of semantics. A person can be known by a variety of names or variations thereof (which is why nearly every package has some sort of AKA statement) and still be the same person. They are who they are. Our job is to be able to document proof of that via the use of satisfactory evidence. But as you said, it doesn't have to be an exact match, it just has to be *good enough* and be lacking any evidence to the contrary. And that takes an individual judgment call from the notary who is having to put their signature at the bottom of the notary certificate (under penalty of perjury in our state, as you know.)
Going back to your example, it's theoretically possible that Elizabeth Jane Doe IS the same exact person as Jane Marie Doe and has been known by both names in her life. (That's why loan packages have Name Affidavits, right?) She still is who she is and may have been the very same person who signed a previous Grant Deed or Deed of Trust in that other name. (Or they could in fact be two different people.) The problem is that she doesn't have satisfactory proof that she's the same person, using evidence that we are allowed to accept. In that case, I'd probably walk.