Michael Jackson named his son Prince because "Prince" was a family name.. Prince the singer has nothing to do with it..
The name goes back for generations on his mother's side. His great-great grandfather, great-grandfather and grandfather were all named Prince Screws. When his family moved north, the name Screws changed to Scruse. Because Prince III had 2 daughters the name skipped a generation... so when Michael had his own children, he decided to honor his mother sejak carrying on this family name!!
so Prince the singer has nothing to do with the name of Prince, Michael's child.