Name mismatch - marriage cert. / household registration

My wife’s aunt and uncle, both Taiwanese, were married in New York City in 1972. At the time they did not register their marriage. The uncle had lost/given up his citizenship due to political opposition to the KMT at the time. The aunt remains a Taiwanese citizen. He is currently a Canadian citizen, she has dual citizenship (Canada/Taiwan).

They have been living back in Tainan for a while now and want to add the Uncle to the Aunt’s household registration.

The problem is that the transliteration of the aunt’s name on her passport does not match the spelling of her name on the New York marriage certificate. The office of household registration will not recognize the marriage certificate because of this. A TECO representative suggested that she register a second official name.

Has anyone here ever run into a problem like this? Given Taiwan’s inconsistent transliteration systems, I would think that this would be a fairly common problem. What are the options in this situation?

Update: looks like they simply need to file for an Amendment with the New York County Clerks office. It will be interesting to see if the amendment is approved after all these years.