Filing a trademark registers a logo or slogan to be displayed on goods or services for public record. Trademarks also are referred to as service marks.The registration of trade names and marks is not legally required in Arizona, but is an accepted business practice. You can file trade names and trademarks through the Arizona Secretary of State website. All companies must file online. Fill Out The Trademark Application. To assign a trademark, the owner must execute a written assignment. Our comprehensive guide on "Trademark Arizona" will help you understand the ins and outs of securing your brand identity in Arizona. To obtain trademark protection in the United States, you must register your company's logo with the US Patent and Trademark Office (USPTO). Anyone creating a business in Arizona will have to register the name of the company with the Arizona Corporation Commission.