Naming your art or craft endeavor can be difficult . . . or really easy. I think it's a lot like naming a band, it can be really fun or a chore. A chore that you put off until you have to have a name for your first gig - then you make something up on the spot.
I made up my business name my last year of college with my first real art show just weeks away. It's a boring name, but its functional - Pottery by Tasha McKelvey. It tells you who I am and what I do.
It also saved me some paperwork.
My choice of a business name included my full name - so I didn't have to file a fictitious business name registration. If a business name does not identify by name who is responsible for the business, then the government wants that business name registered. This process also keeps two business within a certain area from operating with the same name, which would lead to confusion. Back to the naming a band thing - two bands with the same name equals bad.
Note: I have read that a business name must have first and last name or just last name in order to be exempt from filing a fictitious name registration, so please research your local laws on the matter.
Now days, you can usually look up local laws on the internet for your individual localities. There are a lot of other registrations you might need to fill out: business license and sales tax collection registration to start.
With all that said, a made-up name for your business can be really fun. My all time favorite business name is Fat Beagle Pottery. It's in North Carolina and they do have a fat beagle (or at least they did at some point). I have a fat beagle and I'm a potter, but they got the cool name before me. It's in a different state, so I could use the name in my state (unless its copyrighted), but I wouldn't. It would be like stealing in my opinion, but I do love the name.
Warning: Local laws and regulations differ from state to state and even county to county or city to city. Always check to find out what your local laws require of a business owner. This blog is designed to be a forum for suggestions on Art and Craft Business Issues, not legal advice.