Warning: spoilers for Batman: White Knight Presents Harley Quinn #2!
The second issue of Jack Napier, someone she considers a separate person from the villainous Joker.
"Puddin" tends to have an ironic place in depictions of Harley and Joker, underscoring the creepy, off-kilter innocence of Harley's love for a hardened killer who - in the original comics - only cares about her in the context of her utility in his plans against Batman. Here, however, it's recontextualized as something sincere - something which rightly survived Joker, remaining as a testament to simpler, better times for Harley.
Harley recalls the time she first used the name when walking through a place she and Jack went on a date long ago. It was, of course, a carnival. As Harley recalls, she had ordered some pudding that night, a choice that surprised Jack based on all of the other food varieties offered there. Harley playfully retorted by explaining that pudding was classic, just like him, to which she proceeded by saying his ubiquitous nickname. It isn't difficult to deduce that this was the first time she called him Puddin' based on Jack's response: "Please tell me that's not my new nickname." But it is.
Interestingly, this choice by creators Katana Collins, Sean Murphy, Matteo Scalera and Dave Stewart is not the first time writers have chosen to give an origin for the nickname. In HBO Max's Harley Quinn TV series, then-doctor Harleen Quinzel mistakenly believes that the Joker calls her "Puddin" when meeting him for the first time in his cell. In fact, Joker's back is turned when he uses the salutation thinking he's speaking to the asylum chef who's bringing his meal: pudding. It's fitting that Harley's term of endearment for the love of her life possibly stems from a moment in which she misunderstood his selfishness for affection: the brutal problem at the heart of their relationship.
In Batman: White Knight Presents Harley Quinn #2, things aren't as clear cut, as Jack Napier a separate person to the Joker, meaning that here "Puddin" isn't used as a tragic sign of how badly Harley has misunderstood a psychotic super-villain, but rather her desire to hold onto the good person he replaced. It's a valuable differentiation that imagines this Harley as a more tragic hero with a lot more agency - not someone merely fooled by Joker, but someone who truly re him in a different, more complete way than anybody else.