I think some of them are invented by the media, some by enemies and some by friends..

The nickname Bugsy was invented by some journalist (dont know the entire story, but Siegel called them bugs or something like that)

The enemies of Al Capone called him Scarface because of his Scar on his cheek. Nobody ever called him Scarface when he (Capone) himself was around.

Tony Corallo got his nickname Ducks for ducking many convictions. This was a name invented by his boss out of 'respect'.