How to name my business?

I was able to purchase the web domain AMauiPetSitter.com, and tried to register the name A Maui Pet Sitter with the state. They told me the name is too close to Maui Pet Sitters LLC. I call bull, but whatever. Now what should I do? Can I name my business after my own name? Like it would just be "Kandi Smith" on my business card, then my website and contact info?