Rocky Balboa's actual first name is Robert, with “Rocky” used as an alias. His full character name is Robert “Rocky” Balboa.
The name is part of the character's formal identity across the franchise, although nearly everyone calls him Rocky. His son is also named Robert Balboa Jr., which helps distinguish the two in the character's later biography.
Rocky's nickname connects him to boxing tradition and to real fighters such as Rocky Marciano, whose name helped inspire the character's identity. The character is also known by the ring nickname “the Italian Stallion.”
A common mix-up is assuming Rocky is his birth name or that his first name is Rocco. Rocco is associated with Rocky Marciano and appears among Rocky Balboa's nicknames in some character references, but the canonical given name is Robert.