I think that it's worse for Bon Jovi to be referred to as Jon Bon Jovi.
The other way around is just like calling Eric Clapton just Clapton or Steven Tyler just Tyler, people still know who you mean.
When the band is referred to as being just Jon Bon Jovi that is worse as it makes people believe that Bon Jovi is one man.
Technically doing either is pretty much the same though.
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