I agree with the general sentiment, I’d just suggest a minor tweak.
We could definitely do a better job disambiguating the ring-related tags. I’d make one change to your proposal.
Rather than using the generic ring tag for The Ring, I’d create a new tag, the-ring, and use that for the franchise. That way, the generic tag goes away, and it’s less likely that people use it on the “wrong” questions (because it won’t be in the suggested tags). It also avoids future confusion about which ring it refers to.
(I assume that the The Ring question is http://scifi.stackexchange.com/q/26423/3567https://scifi.stackexchange.com/q/26423/3567. When we do the tidy-up, whatever we do, I’d collapse ring and ring-2 into a single franchise-related tag, and let the other tag die.)