Slightly off topic - I can’t imagine calling the framework Sauron and posting a photo from the LOTR movie is legal.
Calling it Sauron is almost certainly OK. Using an image from the movie probably isn't, and the reason why isn't copyright, it's trademark. It makes it look like it may be officially related to the trademark owner. This may sound silly to you, but in a world where the New York Times has an active open source contribution page, along with other non-tech-companies that have put out open source like financial companies, audio companies, etc., the idea that a movie production company might put out a web framework is well within the bounds of possibility. For similar reasons, calling it Sauron is OK but I'd want to lean away from any obvious relationship to the Lord of the Rings, such as posting a satirical version of the ring's inscriptions. (A literary estate putting out a web framework is much less plausible, but on the other hand, they're well known to be on the litigious side, so personally I'd avoid it even so.)
On the plus side, the worst case plausible scenario is a cease and desist, which may never come. Things only get nasty if the project refuses after that.
This is not to say that the holder would still not litigate out of fear of losing their mark, though.
You can probably use Sauron, but you can not literally put up a picture of the Eye of Sauron as your project logo without making it appear that you are operating specifically as that trademark holder. With that picture, they're not just claiming to be "a" Sauron, they're implicitly claiming to be associated with whoever currently holds the rights to those movies.
(I'm only hedging on the "probably" because of the known litigiousness of the Tolkien estate. Normally it shouldn't be a problem.)