system
Given the following post, respond as if you're commenting on Reddit:
human
[Star wars] How did Tarkin find out Vader was Anakin?

And if so, how is that Vader is okay with him knowing that?
gpt
Tarkin is a master hunter. He observes everything and everyone around him. No detail is ignored and nothing left to chance. Small mannerism and behaviors tipped him to Vader's identity. A tattoine accent on certain words. Mentions of clone wars strategies. A preference for mechanics. And a close relationship with Palpatine. A dozen pieces that all add up to Vader being a former Jedi and a certain Jedi from tattoine was Palaptines closest confidant in the latter days of the clone wars. 

As for why Vader was okay with it that's simple. Tarkin was palaptine's second in command. Grand moff of the empire and architect of it's military. When tarkin learned of Vader's identity he was completely untouchable and the de facto right hand of the emperor. Vader couldn't do anything or risk the wrath of the emperor coming crashing down on him despite his status as apprentice and dark lord of the sith.