At least two artists share this name:

1) American choral and orchestral conductor, 1916-1999.

Robert Shaw (April 30, 1916 – January 25, 1999) was an American conductor most famous for his work with his namesake Chorale, with the Cleveland Orchestra and Chorus, and the Atlanta Symphony Orchestra and Chorus. Shaw received 14 Grammy awards, four ASCAP awards for service to contemporary music, the first Guggenheim Fellowship ever awarded to a conductor, the Alice M. Ditson Conductor's Award for Service to American Music; the George Peabody Medal for outstanding contributions to music in America, the Gold Baton Award of the American Symphony Orchestra League for "distinguished service to music and the arts," the American National Medal of Arts, France's Officier des Arts et des Lettres, England's Gramophone Award, and was a 1991 recipient of the Kennedy Center Honors.

2) American blues pianist based in Texas, 1908-1985.

Robert Shaw (August 9, 1908 – May 18, 1985) was an American blues and boogie-woogie pianist, best known for his 1963 album, The Ma Grinder.