It used to be, though, that if people were defining you by something you did years ago, and you didn't want this, you could move to another town far enough way that there wasn't much social overlap between people in your new and old towns.
Unless what you were trying to get away from was a fairly serious crime, there was a good chance the new people in your life wouldn't find out about it unless you told them about it.
Now the old stuff is on the internet, and you can be stuck with it unless you go to more extreme lengths like changing your name.