The reason for keeping their indentities secret is the belief that the artist has to be completely isolated from his audience and his fans. Otherwise he or she might be put under pressure or influenced in such a way that might render all artistic efforts useless. This might be seen as a way of protesting against the way pop music and popular culture have evolved in the late twentieth century, where the artist and his personality have become more important than the contents and the form of his work.
Links:
http://www.residents.com -- RzWeb
http://www.smelly-tongues.com -- Unofficial Fanclub