Todd on a male dog is a specific breed of deliberate humor: the mid-century American everyman name, utterly unremarkable, applied to an animal who presumably deserves something more interesting. The joke writes itself. It also happens to be the name of the fox in Disney's The Fox and the Hound (1981), giving it an old-school Disney reading for those who remember.
The Fox and the Hound Connection
Todd is the young fox paired with Copper the Hound Dog in one of Disney's more emotionally ambiguous friendship stories. Naming a dog Todd is a subtle callback that rewards viewers who remember. Fox Terriers wearing the name carry double irony. See Copper for the complementary pair option.
Mid-Century Everyman Aesthetic
Todd sits alongside Gary, Kevin, and Brad in the bracket of completely ordinary American men's names that work as pet names precisely because of how out-of-place they are. Golden Retrievers named Todd are peak irony.
Counter-Reading: The Joke Only Lands Once
The humor of naming a dog Todd is strongest in the introduction moment. After that, it's just the dog's name. Make sure you love it beyond the initial laugh, because you'll be saying it for a decade without the joke attached.