One thing to consider is if the name is federally trademarked in the same place. For example, you can have an Apple Home Inspection Company, but not an Apple Computer Services Company.
Next you have to check your State's Secretary of State website to see if another corporation, LLC or DBA exists with that name. If so, you can still use that name, just not in that state.
And lastly, you have to consider common law which prohibits deceptively similar names. So, you can't be ABCD1234 Inspections if ABC1234 Inspections exists in your market area.
Here's a video you may find helpful: The Differences Between Patents, Trademarks, and Copyrights.
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