Did Tarkin know that Darth Vader was once Anakin Skywalker?

 Observe the talk between Tarkin and Vader in Episode IV:

Darth Vader: He is here.

Governor Tarkin: Obi-Wan Kenobi? What makes you think so?

Darth Vader: A tremor in the Force. The feeling which I have seemed to notice last was outside the presence of my old master.

Governor Tarkin: He has surely been dead by now.

Darth Vader: Don't underestimate the Force.

Governor Tarkin: The Jedi are dead, their fire has quit the universe. You, my friend are all that is left of their religion.

So indeed there is evidence that: Tarkin knew of Vader’s past as Anakin.