Carl is a name that arrives at the dog park pre-loaded with opinions. It's aggressively ordinary — a name so deeply mid-century American that it carries an instant generational image — and that ordinariness is deployed as humor in the pet-naming context almost every single time. A dog named Carl has an owner who is, at minimum, aware of what they're doing.
The Carl Persona
Carl is the neighbor who always has opinions about the lawn. Carl is the man at the end of the bar who has been there for three hours. More specifically: Carl Gallagher from Shameless and Carl Grimes from The Walking Dead give the name a dramatic dimension beyond its plain mid-western ordinariness. The human name Carl is deep in vintage territory on US baby charts, which is exactly where it needs to be for the pet version to work.
The Comedy of Ordinary Names on Animals
Carl joins Mike, Roy, and Bill in a category of maximally ordinary human names used on pets for comedic effect. The gap between "this name" and "this creature" is the whole joke, and it ages well because ordinary names don't go in or out of fashion. A dog named Carl will still be funny in 20 years.
Breed Fit
Basset Hounds, Beagles, and any dog that looks like it has been through some things carry Carl with maximum effect. A cheerful, scruffy dog named Carl is a comedic masterpiece. Compare with Mike and Roy for similar register.