frankly, I live in a country where only old ones have a religious name (for historical reasons, they are owned buy public entities), the new ones bear the name of a famous doctor, and the free ambulance will send you to the closest public one (unless it's specialized, like extended burns, then it's probably free helicopter to the relevant hospital).

I'm still curious of how carefully selected the publicly available positive statistics on an hospital having a marketing department and operating on a competitive basis are.