What was the other a side of Eleanor rigby?

Eleanor Rigby died "in the church where a wedding has been" while wearing "a face that seemed to face" the congregation, leaving the identity of the woman she really is ambiguous. Father McKenzie, wearing the "black" of formal attire at what presumably is her funeral, may be the other "side" of her; her priest and confessor, he knows much about her that is never revealed to anyone else.