Short phrases fall under trademarks rather than copyrights, and even then it needs to be something that would cause commercial confusion, and very few people are going to buy a Tolkien book expecting a nuclear reactor or vice-versa.
Does it change when one is explicitly a reference to the copyrighted work? It's not like Thiel just thinks that Valar and Palantir and Anduril etc are all just nice sounding words, he's built a brand out of companies named after Tolkien's stuff.