The story
When the types of Rat Terrier were separated by the Rat Terrier Club of America, the short-legged variety was named in honor of Theodore “Teddy” Roosevelt (1858–1919), although he never owned Rat Terriers nor was he instrumental in developing the Teddy Roosevelt Terrier. The dog most attributed to being one of the foundations for the Rat Terriers was a black-and-tan, mixed-breed, feist-type dog owned by the Roosevelts.
Etymology from Wiktionary, CC BY-SA 4.0.