From Wikipedia:
In the
Jim Nabors episode of
The Muppet Show, Kermit briefly reveals that Miss Piggy's second name is Lee, an homage to the actress and singer
Peggy Lee. However, this is the only time (apart from various magazine articles and a Muppet book) that a character calls her
Piggy Lee. Furthermore, in the
Avery Schreiber episode, Miss Piggy "allows" Avery to call her by her real name
Pigathius. Thus, it could be said that Miss Piggy's real name is
Pigathius Lee, although these mentions are one-note comical asides, and don't necessarily represent the history of the character.
Daniel