What about "non-celebrity" celebrity or just "professional celebrity"?
People like Paris & Nikki Hilton, the Cardashian and Gastinow girls... all famous because they are relatives of someone, have money, and managed to find an agent who talked some cable channel into giving them a show.
In a GT game I was in, one of the players was a 'professional celebrity'. He had a letter of credit to withdraw 50,000 cr each month from a trust fund, and pretty much spent his time being wealthy playboy and appearing on talk shows/celebrity romps all over the Imperium (and these were then distributed out from whatever world it was taped on).