From the great book of diners of fanciful design (compare, more generally: restaurants of fanciful design and motels of fanciful design), from Tim Evanson: Charlie’s Dog House Diner, 2102 Brookpark Rd, Cleveland OH:
(#1) The facade, representing a doghouse, with dogs; but this is just one face of the diner, which is otherwise of more ordinary form
Now: on the compound noun dog house; on Charlie’s Dog House Diner; on what is no doubt the most famous dog house in pop culture, Snoopy’s from the Peanuts comic strip; and on diners that have taken dog house entirely for its name value, without any attempt to mimic or represent a dog house — taking the Dog House Diner in Encinitas CA as one exemplar of these. Hot dogs! Getcher hot dogs here!