Should obs be renamed to open-broadcaster-software? Spelled-out names are generally clearer than abbreviations, and I accidentally created a duplicate tag at the full name when doing some cleanup of old mistagged questions.
Keep it as OBS
I've never heard someone refer to OBS as anything other than OBS. Calling it "Open Broadcaster Software" sounds needlessly corporate. It would not surprise me if a significant amount of people didn't know OBS was an abbreviation, and would be confused if we didn't have a tag for it.