The only more recognizable name in the cast than him is Rita Moreno, and that is because she is a legacy carryover from the previous film.
Rita Moreno has been nominated for six Emmy Awards, winning twice (for The Rockford Files and The Muppet Show). She also won a Tony and was awarded the Presidential Medal of Freedom in 2004, so I believe that she is well-known for more than just the Oscar that she won for the original film of West Side Story.