Dr. J. Reko
When Gordon walks into the dental office, the name on the door is "Dr. J. Reko", an anagram of "Joker".
From the DC Animated Universe Wiki entry for "Mad Love", which is the series finale of The New Batman Adventures. It first aired on January 11, 1999. It provides the back story of Harley Quinn, the Joker's girlfriend, and was based on the comic book of the same name. Both the episode and the comic book were written by Paul Dini.
Appears to some to be the real identity of the Joker according to Batman Wikia,
Regardless, Melvin White was linked to the murders of Patrick Harvey and Richard Dent. How the Joker is linked to Melvin White in all of this is up for speculation.
Comic Vine has this to say
Oberon Sexton was an English best-selling crime author and "amateur" detective. He was killed by the Joker who later usurped his identity.
Was the Joker's real name in the 1988 Batman movie starring Michael Keaton and Jack Nicholson.
Jack White is all over several forums with little or no evidence as to where the names came from. Most sources I found point fingers at the name Jack White being Joker's real name. This could be a play on
the White make-up that Joker wears Joker's white face. (Most media portrays Joker as having a bleached white face without make-up)