If you're going to have a website, you might also want to do a web search on the business name. You'll want to see if the URL is already taken.
I wanted my web address to be the same as my business name. Before registering a name I searched all the potential names on line and settled on one that still had the URL available. Then, I registered several versions of the name (with and without "the", .com and .net) before I did anything else.
I found it's harder to find something that's not already out there as a website name than something that's not already registered in your state. If anyone, anywhere is the world, is already using a version of that name in their web address, they'll come up every time someone does an online search for your business.
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