Singer "Rihanna" Fenty is seeking to prevent her father and his business partner from using the name Fenty, which is both Rihanna and her father's surname.
It appears that Mr Fenty and his business partner, through their business Fenty Entertainment, have been alleging links with the singer that do not exist, and may have even been booking her for appearances without her agreement.
Rihanna alleges that their activities will mislead the public and therefore cause damage to her FENTY brand.
Rihanna has registered trade marks in the US for various FENTY marks for a variety of goods and services including beauty and fashion items, promotion and entertainment services. Mr Fenty also has a trade mark registration for the mark FENTY for hotel services though this could be challenged.
US law may differ from UK law in some respects, but under UK trade mark law you would be unable to prevent someone from using their own name providing their use is in accordance with honest practices.
If a court found that their conduct had been in accordance with honest practices then the infringement claim could fail entirely.
Therefore, it is likely that Rihanna is using the applicable US trade mark law as just part of her basis for seeking to prevent her father from using the Fenty family name, and will probably also base her action on their alleged fraudulent conduct.
The lawsuit says Rihanna owns trademarks in the US for the Fenty name and has sent formal "cease and desist" requests.