eg. I am John Smith. I run a company called Fun Designs.
I was reading that in this case (because my name is not the business name i.e. Martha Stewart), it's best to use your private name for your private FB page and then maybe create a linked FB business page for your business.
It doesn't have to be linked though. I personally have already created the business page via my personal page so in my case it is linked. Should I unlink it? Is that possible?