In Spanish and French (and probably some other languages too), you introduce yourself by saying "me llamo __" or "je m'appelle __," both of which literally translate to "I call myself __." I like this, for unlike the passive English "my name that someone else chose for me is," it suggests that you have at least some active role in defining yourself. Here in America, alas, I don't get much chance to exercise the old français, but I do find that it's often necessary to define myself. And it's not easy!
The post-doc is without question the most amorphous and uncertain of stages in an academic's Life Journey (not to mention the most hair-graying, ulcer-forming, and soul-crushing). And with the past decade's advent of even more nebulous terms like "super post-doc," it's more than likely that we struggle with identity issues--especially when faced with the task of defining ourselves, particularly to non-academics.
You grad students and professors have it easy--people have ideas, however misguided, about what it means to be one of those. But how do post-docs tell people who they are? You know, like at parties with people who aren't in science? A fellow blogger recently argued that the term "post-doc" is dead--it's lost what little cachet it might once have had, and is meaningless to those outside of academia, anyway. He opts instead for "short term contract researcher," an expression that sounds to me like the kind of thing you should say if you didn't want to talk to the person anymore. Whoops! Looks like I need another drink / have to find the restroom / remembered I left the stove on! The other thing I don't like about it is that it doesn't convey the fact that you have a schmancy degree! I mean, come on--I once had to fix my Old Navy sandals with a stapler, at least let me impress you with how educated I am!
No but seriously, fair enough--all the term "post-doc" really does say about you is that you should be addressed as "Dr" (something on which you should insist whenever appropriate!). When someone asks me what I do, I tell them that I am a scientist, and smile to indicate that I know how goofy that sounds. They like that, because "scientist" is one of those jobs that might have been in your when-I-grow-up list when you're five--you know: 1) astronaut; 2) firefighter; 3) artist; 4) vet; 5) scientist**. Only the most hardened of souls isn't at least somewhat intrigued by someone who describes herself as a scientist, and then they get to ask you the right questions to help paint a clearer picture of what you mean, rather than you launching into a jargony mish-mash about your PI or whatever.
In the end, I think what's important when we step outside the Ivory Tower isn't necessarily what we call ourselves, but that the words we choose foster, rather than quash, conversation. Scientists have a notorious reputation for not being able to communicate well to the public. If we want that reputation to change, we should at the very least find a way to define ourselves, even when that definition is in constant flux.
** My parents are in possession of paper proof that as a 4-year old I told my nursery school teacher that when I grew up I wanted to "play in institutions." I have no idea how I'd even have known what an institution was at that age, but I mean, way to follow my dreams, right?