Everyone knows Gravano's name but he doesn't count since he is no longer a family member. Since the recent deaths of Gotti and Joe Bonanno, I would say Vincent Chin Gigante is the most recognizable living name in the mob today. As far as I know he's still boss of the most powerful mob family. He's one of the last living links to the old time mob. It was Chin who shot Frank Costello which convinced Frank to retire. Gigante is a big believer in keeping a low profile which is one of the reasons he hated Gotti and tried to whack him. There are still lots of mafiosi out there and they are doing their best to avoid becoming household names. Unfortunately for them, public interest in the mafia, as a source of entertainment, seems to be at an all time high and the media knows that mob stuff sells big time. The NY Daily News actually went to the house of the latest candidate for Gambino boss to interview him about his possible promotion. He was very cordial but denied everything.