Marciano's managers used it somewhere around 1948, after that the nickname was used various times, perhaps most infamously for Stallone's motionpicture. I'm not really familiar with American culture, was it a popular name already before that?
The name is generally used by Italian Americans, and probably derived from the name "Rocco". I'm not sure why it is viewed as a popular name among fighters, but perhaps its because it has sort of a tough sounding twist to it.
It is in fact a derivative of "Rocco". It is also a derivative of the anglicized "Rock". In the 50s it took off in emulation of Graziano, Castellani, and Marciano.
Rocky Kansas was the first world boxing champion called "Rocky" I believe. Lightweight champ in the 1920s. Real name was Rocco Tozzo.
Rocky Kansas was 1 of the 1st but there were a lot of Rockys. Its known as a toughguy name and James Cagney the actor was Rocky Sullivan in Angels with dirty faces, for the ItalianAmerican's its a nickname for Rocco like Nino is for Antonio and Bepe is for Joseph or Guiseppi and Jake for Giacomo a lot of fighters have picked up on it Rocky Lockridge who is black, funny but Bummy Davis got his nickname from Abraham Avroomy to being called Boomy or Vroomy to Bummy and thats Yiddish to American, so most of it is American