The lawsuit claims the company's name "looks and sounds virtually identical" to Unreal and said that was "no coincidence", Engadget reported on Monday.
Epic also said in the suit that the two companies are competing in the same market and suggested the similarity could cause confusion, the report said.
"Epic has 10 registrations for 'Unreal' alone or in connection with another term for a wide range of goods and services including but not limited to software, video games, virtual worlds and 3D visualisations, animations, and platforms," according to the suit.
Nreal released its Nreal Light mixed-reality glasses in South Korea last year and it plans to launch them in the US this quarter, as The Verge notes.
Although Epic doesn't yet have AR hardware of its own, it has shown interest in the AR/VR space.
In 2017, Epic released Robo Recall, a virtual reality game developed with Unreal Engine.
Epic's Unreal Engine is a ubiquitous game-making tool that's also used for films and general-purpose 3D design.
The company is seeking an injunction that would force Nreal to withdraw its trademark application, as well as unspecified damages, the report said.
The companies have been battling over the Unreal moniker for a few years. They had been in discussions over a settlement but weren't able to reach an agreement, according to the suit.