tcoyle writes definitively (7.06):

The reference here - very obviously - is to a flaccid but strangely popular late 1970s comedy bit by Bill Saluga as the cigarette-smoking Zoot-suit and sunglasses wearing creep "Raymond J. Johnson Jr." whose contribution to hilarity was to walk around exclaiming "You can call me Ray, or you can call me Jay, or you can call me Johnny or you can call me Sonny, or you can call me RayJay, or you can call me RJ, but ya doesn't hafta call me Johnson!"
Just Dylan reaching into pop culture.

Helena Michaelson writes (2.05):

As far as I know, nobody has ever dared to called Bobby Ray, but I don't
think 'just for the sake of a rhyme' can be such a bad thing. Have you
heard how bad the jokes in his songs are getting - 'Freddy who? Freddy
or not here I come', etc. What a man.