I don’t KNOW if this is the case with her- but in my family over the generations some have used family names, i.e. last names, as first. Thatcher and Yates could both be old family names.
You have a point.
In my family the ancestors used the mother’s maiden name as the middle name, and occasionally as the first name (Ancestor Caswell Kilby is a good example.)
Problem was, the families intermarried (as good Pennsylvania German Mennonites did back then) and before you knew it the poor kids had first and last names that were the same. I actually have a Zimmerman Zimmerman in my family tree.