When Payam Tabibian, who is known as Peter, sketched his idea for a hamburger restaurant name and logo on a napkin a decade ago, he never thought that his distinctive Z-Burger trademark would be at the center of a legal fight.

He registered the 1950s-style red, white and yellow logo in 2007, before he even opened his first fast-food restaurant the next year in a reviving Washington neighborhood. Mr. Tabibian, 42, who immigrated to the United States from Iran as a fifth grader in 1982, had operated a vending-machine business and sold neckties from the trunk of his car, but he was always passionate about marketing hamburgers.

Beginning as a teenager in Bloomington, Minn., Mr. Tabibian mopped floors at a local Burger King outlet, then, after his family moved to the Washington area, worked at several more Burger Kings and other fast-food outlets, rising to manager along the way.

After studying hamburger marketing, he came up with the concept for a lively, accessible store that tied itself to the local community with contests, food giveaways, fund-raisers and happy hours. His marketing pitch: Z-Burger’s hamburger patties are made of a unique meat blend, the buns are specially baked, the fries are doubly cooked and the milkshakes are extra-rich.