If I may! Gaylord is actually a name people (used to) have in English, appearing as both a given name and a surname. As far as I can tell it's derived from the older French name Gaillard. I'm only speculating, but I think at the time this toy was marketed, the joke was more "look at this dog that has the name of a person! A very old-money kind of person! It's even funnier because the dog is sad and has no dignity!"

And now it's funny for other reasons.