Harley has a handful of nicknames for the Joker, with “Mista J” and “puddin'” the most prominent. Most have chalked up the names as remnants of her frequently put upon singsongy, working-class New York accent, but the puddin’ name has been canonized over the years. They honestly could have gone without explaining it as it’s not uncommon for someone to call their paramour “sweetheart,” “pumpkin,” or even “snookums,” but this is a character in a world created by comic books … of course, there’s going to be an eventual explanation.
In “Batman: White Knight: Harley Quinn #2,” it’s explained that the nickname was given to a non-Joker Jack Napier, as he is as classic as the dessert treat. He even jokes, “Please tell me that’s not my new nickname,” knowing that it’s going to stick. Harley’s insistence in calling him puddin’ even when he returns to being the Joker is presented as her way to remind herself that he’s still Jack underneath the makeup, and perhaps her attempt to remind him of who he is capable of being.
To contrast, season 2 episode 6 of “Harley Quinn” sees that it’s Joker who calls her puddin’ for the first time. She approaches still as the psychiatrist Dr. Harleen Quinzel, but the Joker mistakes her for someone else and says, “Hello, Puddin’.” Quinzel is confused and says, “Puddin’?” with a meek, almost impressed demeanor, to which Joker then replies, “Oh s***, I thought you were the person who brought my lunch.”
So why does Harley Quinn call the Joker a nickname that equates to her calling him a Snack Pack? It’s up to your own interpretation.