Simpsons Wiki

Les Moore[1] is the original owner of Santa's Little Helper running at the Springfield Downs Dog track. After Santa's Little Helper lost on Christmas Eve, he abandoned him in the parking lot and Homer and Bart decide to adopt him.[2]

― Les's Catchphrase
Can I offer you a drink to throw at my face?
― Les Moore
There you are, old pal.
― Les Moore

After Santa's Little Helper became the new mascot of Duff Beer, Les came back and claimed him again to get the money the dog was getting. Eventually, when a new mascot for Duff Beer was found, he let the Simpsons have him again due to him being worth no money any more.[3]

In the book, "The Simpsons: One Step Beyond Forever", it is revealed that his first name is Les.

In the episode “The Way of the Dog”, his last name was confirmed to be Moore.