Your initial instinct was correct: no legal name changes in San Francisco, and the reason is, as you found out, that SF doesn't hold judicial ceremonies.
So let's start with "I'm not a lawyer" :-)... but based on the limited amount I've read, your wife's legal name never changed. A Naturalization Certificate is not a valid name change... what I mean is that if your name is Alex Win and they print Alex Gin on your Naturalization Certificate, your name is still Alex Win and legally (as far as I understand) all your other documents would have to say Alex Win. So I'm not really sure if your wife registered to vote in her legal name or not... what a headache!
The only legal basis for what the interviewer did (as far as my limited understanding goes) was to assume that he considered this a marriage-based name change and accepted your country's marriage naming convention. This was nice of him; but will be a headache for you.
Easiest solution at this point: file for a name change in court for a change from the original name to the name on the Nat Certificate. That way you get a nice legally-binding name change order and your wife can get all her documents changed over to the new name. There's no way to get a name change certificate from USCIS because they don't have the authority to change names. There's no way to get a copy from a court, because no name change order was eve issued. So it's basically a new name change application. It'll be odd that the certificate will have a later date on it than the nat certificate, but I doubt (although I'm not sure) that anyone will care.
