The longest continuously named road in the U.S. isn't Sunset Boulevard, although it can sometimes feel that way when stuck in traffic on the 2 bus. Sunset is 22 miles,
narrowly missing the big win. I can't find a better resource on the length of New York's Broadway than Mapquest -- but if you follow it from Battery Park ("1 Broadway") to where Broadway becomes the Albany Post Road (adjacent to the Rockefeller State Park in Tarrytown), it's 33.62 miles. However, it bears the names "North Broadway" and "South Broadway" a few times in between, and is better-known as U.S. Route 9 for much of the trip. Sounds fishy to me. The real title belongs to Denver's Colfax Avenue, at 26 miles.
I mention this because my friend charltonlido, who lives in London, speculated that the 11-mile Whitehall Road was the longest such road in England. (Amateurs, I thought, until another acquaintance offered "Peterborough-Grantham Great North Road: about 31 miles." Some debate followed over whether citing the entire 409-mile length of the A1 would be cheating.)
Edit: Sepulveda goes 31.7 miles without changing its name. Take that, Denver!