The Gold ‘N Silver Inn in Reno, Nev., has long offered health coverage to its employees — but many of the cooks, dishwashers and waiters who make close to minimum wage can’t afford the $100 monthly premium. Last January, when Nevada became one of more than two dozen states to expand Medicaid under the Affordable Care Act, 10 of the diner’s 55 employees qualified for the government insurance program for low-income Americans. None of them realized it, however, until the family-run restaurant hired BeneStream, a New York-based start-up funded partly by the Ford Foundation. BeneStream charges $40 to screen each...