Katherine, most people get a DBA (doing business as), which is the name that you would use when applying for your business license. Usually that happens through your local area. As long as someone else in your area isn’t using the name, you should be able to use it. It would be possible for multiple businesses in Iowa to have the same name. If you register it as an LLC, which I really don’t think is necessary, then it would likely need to be unique and not be the same name as any other corporation in Iowa.