Finley (Fennelly?)/Birmingham

Hello! My great great grandmother Bridget Caufield’s (~1854-1928) New York death certificate lists her parents as Michael Finley and Mary Birmingham. Her obituary lists sisters Catherine Gilhooley, Mary Ryan, and Margaret McManus. Bridget is also listed as "Mary" in a couple of census documents.

There is a New York death record of a Catherine Gilhooley (~1878-1940) with parents Michael Fennelly and Mary Bermingham (her obituary does not provide more information, so I haven't confirmed a relationship to my Bridget yet. . . still working on it).

A search of RootsIreland reveals baptism records for Mary (1858), Catherine (1861), John (1864), and Margaret (1866), children of Michael Fennelly and Mary Bermingham of Ballinalina, parish of St. Canice’s in County Kilkenny. Another baptism record exists for Catherine (1869), child of Michael Fennelly and Mary Bermingham of Reyewfield, parish of St. Patrick’s in County Kilkenny (likely Reviewfield, close to Ballinalina?). My first question:  Could this be the same set of parents, or is it more likely there are two Michael Fennelly/Mary Bermingham families, each with a daughter Catherine?

I have not found baptism records on RootsIreland for my Bridget, so I don't know where she was born.  I just know the names of her parents as reported on her death certificate. My second question is whether it's reasonable to consider that Finley was recorded as a variant of Fennelly.  My third question is therefore similar to the first one:  How likely is it that there might be multiple Michael Finley (Fennelly)/Mary Bermingham families with daughters with these names?  I haven't found any such overlap yet.   Any advice or thoughts would be much appreciated!

Thanks!