That's a very good example. I think it primarily relates to who had the creative control in a band, as sometimes it was shared and more often one or just two members. There are even examples of the main exposure and success was sometimes outside the artists themselves, as in producers and songwriters. I just did an article on the Four Tops. After Holland-Dozier-Holland (their primary songwriters) quit Motown, their popularity and success fell off sharply. The Four Tops had great vocal talent, but little to no songwriting talent.
Jefferson Airplane.
As the roster changed Jefferson Airplane first changed their name to Jefferson Starship, then when the last original member left they dropped Jefferson and went by Starship. Their musical styling had also changed from Acid Rock to Commercial Pop.