What's in a Last Name?

Writing about HP and slapping together a Peanut Butter (that's what my wife and I call a peanut butter and honey sandwich), the catalyst for this post drifted into mind.

I mean, really, where do people come up with their last names? Are they born with them? Do they make them up? Are they knighted with or have them conferred upon them?

I have heard it rumored that last names originally had an occupational association tied to them. E.g. I have often been told (and read for that matter, if having "read" anything makes it fact) that Fletcher means a maker of arrows.

To me, this makes sense. Thus, a person named Smith is someone who makes stuff. But then carrying the deduction a step further, is a Potter someone who plants flowers or other plants into soil? And what about a Longbottom, for that matter? (On second thought, let's keep that question rhetorical.)

I'm sure that Scalois will be able to come up with some awesome archeological digs (or at least some interesting links). As for the rest of you (and as always on the C.A.), please share your thoughts and insights.