In my state it is the secretary of state’s office. On that web site you will likely find a link to business services or similar. In that area look for name search, name registration, etc etc
Our Superior Court Clerk registers trade names for the county. We can go into their books . . . same roon as real estate deeds and plats . . . and look them up.
Just googling it will often provide info as to whether or not it’s being used. Of course, it’s no guarantee.
Go to the uspto website and do a search to see if it’s been trademarked (or look for similar, as any attempt to register a similar name trademark will most likely be rejected for "likelihood of confusion with existing mark.
