Alpha and Omega

On my way back to the airport in New Orleans, I spotted a squat, bright blue glass building to the side of I-10. It looked like it had been transported directly from the early 70s and was vaguely the worse for wear. In 1 story high letters on its side: Omega Hospital. It was all a bit offputting and I couldn't quite figure out why, until the phrase "the alpha and the omega, the beginning and the end" wafted through my brain. Why would you name a hospital for something that evoked "the end"?