Filing Length: Trade Names last for 5 years from the date of receipt. Trademarks last for 10 years from the date of receipt.The registration of trade names and marks is not legally required in Arizona, but is an accepted business practice. Fill Out The Trademark Application. Although federal registration of a trademark is not mandatory, it has many advantages over common law trademark rights. Rights created under federal law. Trademarks must be in use prior to filing the trademark registration application. 4. Pay for registration. To assign a trademark, the owner must execute a written assignment. If you're ready to trademark your logo, the first step you should take is to conduct trademark search.