Redford portrays 'The Sundance Kid' in Butch Cassidy and the Sundance Kid, which is one of his more famous roles. The movie came out in 1969. He co-founded the Sundance film festival in 1978. Did he name the festival after the character or does the name have another origin and the similarity is a coincidence?
Yes. According to Wikipedia, it was called the US Festival until:
In 1991 the festival was officially renamed the Sundance Film Festival, after Redford's character The Sundance Kid from the film Butch Cassidy and the Sundance Kid.
Time Magazine offers more information on the matter:
The festival changed titles frequently — from the U.S. Film Festival to the Utah/U.S. Film Festival to the United States Film & Video Festival to the Sundance/United States Film Festival to, finally, Sundance. The last two changes came about after Redford's Sundance Institute took over the festival in 1985. Redford, who owned property in Utah's Wasatch mountains, named the organization after his character in Butch Cassidy and the Sundance Kid