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I really think the only reason people talk about "Hillary" is because "Clinton is running for President" would be confusing. None of the terms used to distinguish the Presidents Bush, e.g. "Daddy Bush" and "Baby Bush," are any more respectful (not that either of them deserves much respect, but that's another matter) and I don't remember anyone talking about the "Mondale-Geraldine ticket" back in 1984.
Anyway, call her what you will, I'll vote for her if she gets the nomination, because she is guaranteed to be better than anyone the Republicans are going to nominate. Seriously. She's way too far to the right for my tastes, but Clinton vs. Giuliani or McCain or Romney or Thompson or any of those nutcases is like your annoying neighbor vs. Joe Stalin.