In what is expected to be a multi-million dollar lawsuit, attorneys for the California band are seeking an injunction that would stop Cowell's 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.

The five Britons, who have taken the U.K., the United States, and Australia by storm after being discovered on Cowell's British talent show "The X Factor" in 2010, are named along with Syco and Sony Music Entertainment in the federal lawsuit filed on Monday in California Central District Court.

The California band says it is entitled to three times the profits made by their rivals, as well as compensatory damages in excess of $1 million.

Syco declined to comment on Tuesday, and a representative for Sony Music could not immediately be reached.

The lawsuit claims that Syco and Sony Music "chose to ignore the plaintiff's rights and wilfully infringed them" after they realized in early 2011 that the two bands share the same name.

The northern California band has been using the name One Direction since late 2009 and has recorded two albums, the lawsuit states. It filed an application to register the trademark name in the United States in February 2011.

The British band, made up of Niall Horan, Zayn Malik, Liam Payne, Louis Tomlinson and Harry Styles placed third on "The X Factor" and went on to top the U.K. charts with their first single.

Their debut album "Up All Night" entered the Billboard charts at No.1 last month in the United States, and they were greeted by hordes of screaming young girls at appearances in New York and Los Angeles ahead of a U.S. tour later this year. They are currently in Australia.

One Direction already has some 4.2 million Facebook fans and 2.8 million followers on Twitter.

The five man California band, by contrast, has a much lower profile. Led by singer and pianist Sean O'Leary, its members began making music at school and the group has played at local fairs and bars, according to their website.

The lawsuit said the continued use by both bands of the same name was causing "substantial confusion and substantial damage" to the goodwill earned by the California group.

(Reporting By Jill Serjeant; Editing by Bob Tourtellotte)

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