From what I've read about it, it sounds like the name of the pub isn't really the issue and that the movie company would have a hard time getting them to change the name, however the additional use of images from the book/film and the names for menu items plus "dressing" is an issue as they're really trading off the Tolkien brand.
Hopefully they just come to a reasonable price to license the existing usage and keep things going. That way pub gained free PR (how many of us had heard of it before now
plus movie company doesn't come across as the big evil giant stamping out the little guy (even if they are just protecting what is really theirs)