Filed on Monday, the federal lawsuit names the five boy band members together with Simon Cowell's management company Syco and record label Sony Music Entertainment.

Attorneys for the California band are seeking an injunction that would stop Syco Entertainment and Sony Music from using the name One Direction in promotional materials. They also want a share of the profits earned by the chart-topping British boys.

According to the lawsuit, the rock band has been using the name since 2009, recorded ...