The Bob Marley Foundation and 56 Hope Road Music Limited have filed a lawsuit in the Commercial Court against entertainer Fabian Marley.
The Bob Marley Foundation controls the rights to the Bob Marley name in Jamaica, while 56 Hope Road Music controls the rights to the name in the rest of the world.
News emerged last month that a DNA test revealed that Fabian Marley is not the son of the reggae legend.
In the documents filed in court on Wednesday, the companies are seeking an injunction to prevent Fabian Marley from using the Bob Marley name or associating himself or any of his business activities with Bob Marley's name or image.
The court is also being asked to order Fabian Marley to stop using the name Marley and to change his last name.
They are also seeking damages for Fabian using the Marley name for personal gains.
The court documents state that the defendant was named Oniel Stanford when he was born in 1968 and changed his name by deed poll in 2012.
They posit that Fabian Marley markets himself as the son of Bob Marley, which is likely to lead the public to believe that he and his music are associated with Bob Marley. They say he has been asked repeatedly to stop using the name, but has refused to do so.