After the Joker died in City of Broken Dreams 2 - Payback Time, Jack Napier attacked Humane Labs. But he suffered heavy burns during that, get caught and fled from the hospital in Sandy Shores.
His disfigurement led to the decision to wear a mask, and thus the Masked Marauder was born. Jack Napier uses this name himself, as he addresses his plans in a tv broadcast nearing the end of the movie “The Shady Avenger”, but it is a name he has been given to by the Avenger. Thus it is not known how he planned to call himself in the first place. He abandons mask and name soon in the movie “Finance & Felony - The Movie”, so the name obviously didn't sit too well with him.

The Shady Avenger
Finance & Felony - The Movie