Rihanna has been making money with the family name. She crossed over from being a pop star to a beauty mogul. She owns a makeup and lingerie line. But her father wants a piece of the pie and has been using the family name and suggesting that his famous daughter might be involved. Rihanna says he is tarnishing her reputation with his shady business practices, and some of her fans feel father or not, she has every right to sue.
But everyone is not on Rihanna's side. The name Fenty belonged to her father first. People argue it's ridiculous for Rihanna to think she can sue her father over a name he gave her, and suing your parent is just tacky.