Duckie is an affectionate diminutive in British English, a term of endearment like "darling" or "love," that also points toward actual ducks, and occasionally toward Duckie Dale from Pretty in Pink. Any of these could explain the 36 registrations, though the most likely origin is simply that someone's puppy waddled like a duck and the name attached itself before anything more formal was chosen.
The British Endearment Reading
"Hello, duckie" as a greeting is a distinctly British register that American owners sometimes adopt with full awareness of its foreignness. Applied to a pet, it reads as warm, slightly theatrical, and gently ironic. The name suggests the owner addresses their pet in the manner of a charming British sitcom character.
The Duckie Dale Reference
Jon Cryer's character in Pretty in Pink (1986), the devoted, slightly eccentric best friend who loved Andie in all the wrong ways, gives the name a 1980s film register. A quirky, devoted male pet named Duckie might be honoring that specific nervous energy.
Sound and Breed Fit
DUCK-ee is easy to say with affection and impossible to say with authority. Works on small, waddling dogs like French Bulldogs and Corgis, or any pet with an endearingly awkward gait. Also completely accurate on actual pet ducks, should the registry capture those.
The Counter-Reading: Entirely Unkempt for Authority
You cannot discipline a dog named Duckie with any credibility. This is a design feature for owners who have accepted they are not actually in charge.