How did nicknames become surnames?

There seems to be some confusion here - - names based on geography are NOT generally "nicknames". A nickname would generally be based on some trait or characteristic (or perhaps event) of an individual or family, generally something distinctive, perhaps quite unusual Nicknames became one way to distinguish one guy named Joe from another. One Joe may have red hair, so he may have been called Joe Rosa (Latin for red) or Joe Reddish, or Joe Barbarossa (red beard). Another Joe may have been a mechanic, so he'd be Joe Smith (mechanic) or Joe Blacksmith, or Joe Black. Another Joe may have been a baker, so he'd be Joe Baker, or Joe White (for the flour). Another Joe may have been the son of John, so he'd be Joe Johnson.