Should I be concerned about using a company name that already exists?

The fact that someone else in another state is using a similar name is unimportant.  There are thousands of businesses whose name includes the words "acme" or "premium" or something similar.  What is important is whether the name being used by the other company is a trademark, and if your use of the name would violate the trademark (not knowing the name, I can't opine as to whether it could be trademarked).  The first is possible, but the second is unlikely. You can run a trademark search to determine if the other company's name has been registered as a trademark, but it is possible for the name to have acquired trademark status even if not registered (the trademark owner's riemedies for infringement would be less than if the mark was registered), even if that were the case, from what you've written, your use of the name would not infringe the trademark. The idea of trademarks is that consumers should not be fooled into thinking that two businesses using similar names (or other trademarks, trademarks are not limited to names) are connected, so that one doesn't trade on the goodwill owned by the other.  Consumers are unlkely to be so confused where the businesses sell different things or operate in different markets.  Thus, registered trademarks are registered for particular product classes.  While  Boston Market may have have a trademark on the name "Boston" with respect to fast food restaurants, that doesn't prevent a brewery from marketing Boston Lager.  Eastman Kodak may have a trademark for Kodak with regard to cameras, that doesn't mean that a travel company could not use the name "Kodak Tours."  If you are in a completely different business than the other company, you would not be violating any trademark by using the name.  Also, not all trademarks, particularly common law trademarks, extend over a wide geographic area.  Mario's pizza restaurant operating one restaurant in Iowa could not prevent a restaurant in Hawaii from using the name Mario's pizza restaurant - the Iowa customers are unlikely to patronize the Hawaii restaurant, or to be confused into thinking the two restaurants are connected if they do.