Every US state runs a free, public database of registered business entities, usually maintained by the secretary of state. Searching a name there shows whether a matching entity exists, when it was formed, who its registered agent is, and whether it is in good standing. These databases are the authoritative source, not search engines or third-party directories.
If a name returns no match, the careful conclusion is narrow: no entity under that exact name is registered in the states you searched. It does not prove the name was never used, and it says nothing about domains, which are registered separately from businesses. Domain ownership and company registration are different systems with different records.