DC can also be turned into a dog's name, but there are some limitations. One is that DC is really just an acronym for Detective Comics. That, in itself, doesn't make for a very compelling pet dog name. Still, you can simply use the acronym without committing to what it stands for in the comics.
Alternatively, you can turn to other dog characters in the DC comics as inspiration. For instance, you can name your dog after Krypto, the super-powered dog that became Superman's loyal sidekick. You can also just use human names of DC superheroes, like Barry (after Barry Allen, who is the Flash).