Prince was the name of Michael's grandfather (Katherine's father).
Probably he named his sons Prince after him.
Anyway MJ and Prince respected each other despite the rivalry, which was more perceived by the medias than the artists themselves.
Prince the eldests offical legal name is michael joseph jackson Jr . His nickname is prince after michaels grand and great grandfather. The youngest sons legal name is prince michael jackson. But nicknamed blanket. Now know as bigi.
Nothing to do with prince the singer. Its origins are from slavery