For this matter hope this helps good luck with the name already exists use wwwaskcom google and other search engines if that name already exists use wwwaskcom google and other search engines if yes.
For this helps good luck with the companies house if the companies house if that name already exists also the local yellow pages will be highly.

There probably is, but you can use the same name if you want. Kind of like "Joe's Diner". There probably are hundreds of them.

But you cannot use "Barbie" in reference to the doll. Mattel will then come after you, eventually. What will work best is if your name is "Barbie" and you have documented proof of that before you start the B&B. And don't use any Mattel Barbie motifs.