Resident Evil isn’t the “original” name, since the Japanese version calls the entire series BIOHAZARD. Only versions outside Japan call and refer the entire series as Resident Evil. They’re exactly the same game with the difference being the name. I think BIOHAZARD refers to the end game sequence (in most entries in the series, but not all) where they find the lab that’s owned by Umbrella Corp.
You know, I was lurking around in all, and saw this and immediately thought, this is wildly interesting. I’ve played since the original and never knew why. So, it’s super lame. Trademarks. A communications director said it would be hard to get the TM in USA, so Capcom voted to change it to Resident Evil internally. The name was picked because it took place in a mansion. You are correct in that, BIOHAZARD refers to the end game with Umbrella.