What is the meaning of 份 in 身份? Is 份 used as a word pointing to a papers i.e. documents (passport and so on)? Or is it used as a 'division' so as to differentiate a man from man (身 body in our case)?
In the past, it was 身分, which means the social position of an individual.
Somehow, in modern times, it evolved to 身份. Indeed, in Taiwan, the identity card is called "身分證", while in Hong Kong, it is called "身份證".
I would say that both "身分" & "身份" have their supporters.
If you can read traditional Chinese characters, there's a pdf about the controversy over "分" or "份" in the translation of "identity card", by the law drafting division, Department of Justice, of Hong Kong.
Have fun :)