Lyric discussion by DollarShort 

Cover art for Marlon J.D. lyrics by Manic Street Preachers

I would say the "J.D." of the title does refer to James Dean, and is initialized for a reason. Like MBlack said, Dean and Brando were cut from the same cloth. Whereas Marlon Brando lived on, becoming a grotesque self-parody, James Dean's life was shortened in his prime. Therefore, the title could be seen as two sides of the same coin, one abruptly cut-off, one allowed to live on with dubious consequences.