The Idaho Falls Giant has no name, but he does have a plaque that states Peter Toth's goal of carving a similar statue for each of the 50 states. The Smithsonian Institution website indicates that the supplies were donated by local businesses and Governor John V. Evans presided over the dedication ceremony on November 18, 1980. The sculpture appears to be in terrific shape today.
Artwork - Sculpture
Links: www.waymarking.com, en.wikipedia.org