Thank you all for the responses! Just to bring this back on topic a bit - she was actually born here in NY, but her parents came from either Belarus or Russia - unfortunately don't have more details than that. Hope that is helpful on tracing down some details on the name, thank you again - please keep the ideas coming!
Do you have more information about the specific location? With borders that changed throughout the years and different regions having more of a Ukrainian pronunciation and some more of a Litvish pronunciation, things can change. However, with this specific name, the two yud discussion seems irrelevant, so it's more of a question whether it would be spelled with a צ at the beginning or a טש, as well as whether there would be a yud just before the final aleph.
I brought you just one sefer, there are definitely other seforim that discuss rules as well as specifics of names, as these are very important for gittin.
If you have time and want to look around a little, you might do some searching at
https://www.jewishgen.org/databases/Belarus/ (or some of their other databases)
For example, you might find:
or
and use that as a starting point.
You can also find some US gravestones such as:
http://data.jewishgen.org/imagedata/jowbr/USA-02269/MSC46.jpg but I'm not sure if I'd use that as a source.
Based on what I've seen so far, I would guess that the correct spelling is ציזא, however, since you're probably not looking for the spelling to put on a critical document such as a Get, I'm not sure if further research is justified.
As far as the etymology of the name, I am totally clueless. Some seforim do have that.