How did this breed of chicken get it's name?

Isaac C. Wilbour is given credit for naming the breed. Dr. Brigham and Samuel Cushman of the Agricultual Experiment Station visited Wilbour's farm sometime in the late 1890's and is said to have had the following exchange: "Mr. Wilbour, you have a new breed here and the time has come to give it a name. Have you a name to suggest?" Wilbour replied, "Why wouldn't Rhode Island Reds do?"

Rhode Island Reds

I like your answer better.

Well, this is what I had:

The origin of the Rhode Island Red dates to a fowl bred in the section of New England that is located between Narragansett Bay and Buzzard's Bay. The name Rhode Island Red was given the breed in honor of the state where it originated from crossing the Red Malay Game, Leghorn and Asiatic native stock.

http://www.urbanext.uiuc.edu/eggs/res10-breedhistory.html