Originally Posted by
rustykettel
Does any of the original immigration paperwork or her original Chinese passport have her name in hanzi characters that might show a continuity? It looks more like a difference in romanization than a name change. Maybe try contacting the embassy/consulate again and ask how they handle romanization differences, particularly between Wade-Giles and pinyin (what Tsui and Cui look like to me).
Not specific to a Chinese visa, but the US Passport Agency wouldn't accept my wife's name post-marriage with just a marriage license because it was non-standard. She ended up doing a legal name change process, even though her name was already legally changed (DMV, social security, etc. all accepted her name), so she would have a court document showing the old name and new name. It took about two months and ~$150 in our jurisdiction but it done and settled now and she was able to do it on her own without a lawyer's assistance.
On the observations page of her father's passport he has a remark that says his last name can also be spelled as Tsui. Unfortunately her's doesn't have that same observation, however we showed the Visa agent a photocopy of his passport and tried to explain it was the romanization issue you mentioned to no avail. The agent insisted that we had to bring in a document from a court ordered name change. The only reason we didn't push the issue is because my wife didn't know if one existed or not, but after calling the courts we now know that it absolutely does not.