What exactly are you hoping to find ? What is "confusing" ?
We may be able to help in some other way. 
The information I was given is that Mary was b C1884 in Auckland
Without a middle name I found only the one
RGO/B: 1884/14883 Kennedy Mary Jeanie William [b.10Sep1884]
RGO/D: 1974/31780 McPhail Mary Cecelia 10 September 1884
Marriage=Charles McPHAIL md.1910 Mary Cecelia MEEHAN
I'm thinking that Mary MEEHAN is not mine because of the marriage year, but the same birthdate has muddled me.
I agree that the Mary KENNEDY (10 September 1884 birth, registered at Auckland) and the Mary Cecilia McPHAIL (nee MEEHAN) death record with the exact same birth date, is peculiar.
What I find equally odd, is Mary KENNEDY married Rupert Sydney FOOTE in
February 1906 ... he left her in
1908 ... and yet a Divorce was not sought until
1914 (2 years before he re-married).
I'll get back to you again when I've sorted out a few more records.
[Have previously looked at electoral rolls for the FOOTEs (perhaps that should be "FEET"
? ) ... and I thought I'd found Mary some years after husband left, working as a barmaid ?? [Lost her in the 1920's though and ran out of time to check further. ]
Find it hard to believe she would have involved herself in divorce proceedings, (and exposed herself to the risk of being found to be a bigamist) if she'd earlier remarried (1910) and had several children with 2nd husband by 1914.
A change of name wouldn't be a surprise (many a woman used this ploy to avoid a divorce ... and then remarry.)
~ Lu
