That Thiel named his company Palantir has always struck me oddly.
In the books, the palantir were "seeing stones" gifted to men by the elves, and could be used to see events remotely, and to communicate mind-to-mind by users. But after Sauron acquired one, using them became perilous as the Dark Lord could limit what users saw, effectively controlling their information flow, even if he could not overwhelm or twist them directly via the mind-to-mind contact. While Aragorn does manage to wrest one free of Sauron's control, allowing him to save the day at a key moment, overall they are a powerful tool for the forces of evil.
I think it's just because he had no illusions as to the good and bad uses it would bring. I've used Palantir Foundry heavily at work, and it is good for remotely viewing events and communicating mind-to-mind to executives with pretty dashboards. Definitely nicer optics than their Gotham platform used by USA law enforcement since e.g. it helps Airbus identify issues on their plane fleets before they occur.
Plus from talking to the Palantir engineers, the CEO and Thiel are both weirdo nerds, so it's fitting.
It's not even the specific name, but simply using any name from Tolkien.
Tolkien didn't like the consequences of technological progress. While engineers were not inherently evil in his works, they were at a high risk of becoming evil, or at least instruments of evil. Think of characters like Sauron and Saruman, or Fëanor and Celebrimbor. If you give a Tolkienian name to your tech company, you are implying that you are one of those guys.
If you realize that Peter Thiel intends to use Palantir exactly for that purpose (controlling information flow, and as a surveillance system), it makes complete sense.
In the books, the palantir were "seeing stones" gifted to men by the elves, and could be used to see events remotely, and to communicate mind-to-mind by users. But after Sauron acquired one, using them became perilous as the Dark Lord could limit what users saw, effectively controlling their information flow, even if he could not overwhelm or twist them directly via the mind-to-mind contact. While Aragorn does manage to wrest one free of Sauron's control, allowing him to save the day at a key moment, overall they are a powerful tool for the forces of evil.