Could be either human's name or a pet's name.
In the Disney version, it is Bruno.
Rufus is a not a common name for dogs. As it has no meaning or history , it is rare to see that named dogs. Though it is sounding nice and catchy it is not that popular , but surely one can consider this name for dog.
Rufus Wright's birth name is Rufus Gerrard-Wright.
Rufus McCosh's birth name is Rufus E. McCosh.
Rufus Wainwright's birth name is Rufus McGarrigle Wainwright.
Rufus Sewell's birth name is Rufus Frederick Sewell.
Rufus Bess's birth name is Rufus T. Bess Jr..
Rufus Le Maire's birth name is Rufus Ralph Goldstick.
Rufus Hound's birth name is Robert Simpson.
Lynx rufus or Felis rufus
Rufus (Latin for 'red head')
You can name your dog anything, but common names are: Max, Fido, Stella, Cocoa, Mutt, Sam, Bingo, Spot, Chase, and Rufus, etc.