This is my understanding - Under Hoover, the FBI had denied the existence of "the Mafia" for years. But that became harder to do after the Appalachin bust. I remember reading a comment by some official back around that time that said something like, "There's no Mafia but there is a La Cosa Nostra and we've been keeping tabs on it for some time." Apparently a way to save face. Even though it was referred to as "Cosa Nostra" in the FBI's own records, and later identified as such by Valachi, they came up with "La Cosa Nostra" so they could use the acronym "LCN" is their reports, despite it being grammatically incorrect.