What about the other non-Doo Scoobys? For instance, Scooby Dum and Scooby Dee.
It has been proposed here that Scooby is the family name while Doo is the given name, as in Chinese tradition. Scrappy Doo, Scooby Doo’s nephew, would be the son of one of Scooby Doo’s sisters and an unknown dog with the family name of Scrappy. This page is very interesting and puts forth the hypothesis that Scooby Doo is an example of the ‘Dogs of Fo’, highly intelligent dogs that inhabited eastern China, said to resemble Great Danes (this makes sense, as such dogs would have to be very large to support their larger braincases). This breed was created by Fo Hsi, emperor of China in 2852 B.C., who created the I Ching and contributed greatly to Chinese knowledge of animal domestication.
There are problems with this theory, as the author apparently was not aware of all of Scooby Doo’s relatives and how they were related to each other. It does appear that Doo may in fact be the family name, see this list of Scooby’s relations…
Scooby Dum, cousin
Scooby Dee, cousin
Scrappy Doo, nephew
Ruby (Rooby) Doo, sister and Scrappy’s mother
Grandpa Scooby
Yabba Doo, Scooby’s brother
Whoopsy-Doo, cousin
Dooby Doo, look-alike cousin
Dixie Doo, cousin
Skippy Doo and Howdy Doo, brothers
All of Scooby Doo’s siblings share the name ‘Doo’. Not all of his cousins do. ‘Scooby’ also seems to be a very common name in his family, perhaps in honor of ‘Grandpa Scooby’ (I personally believe that Scooby Doo’s grandfather may also have been named Scooby Doo, and the most famous Scooby Doo might actually be Scooby Doo III).