J. Edgar, Junior (abbreviated as J. Edgar, Jr.) was a nickname that Marty Neil earned while studying at the FBI Academy in Quantico. In 1993, the name was used in reference to Marty Neil by his former classmate, Dana Scully, while she was dining with another of their former classmates, Tom Colton. (TXF: "Squeeze")

Presumably, the name was deliberately meant to sound like the president's name, J. Edgar Hoover. It is not known how many people knew Marty Neil as "J. Edgar, Jr.", besides Scully and Colton.
The subtitles from The X-Files Season 1 DVD spell the name as "J Edgar Jr".