Is Anakin Skywalker Darth Vader?

So, the main question is, is Anakin Skywalker identical with Darth Vader. In other words, for every property that Darth Vader possesses does Anakin Skywalker possess? (I owe this question to my friend LJ.)

The primary puzzlement about this question is a statement by Obi Wan Kenobi - Darth Vader is more machine than man. Anakin Skywalker was a man, and then was dubbed Darth Vader by Emperor Palpatine upon Anakin Skywalker's conversion to the darkside of the force. Now, if we follow Saul Kripke on names then both 'Darth Vader' and 'Anakin Skywalker' are rigid designators. That is, names are not descriptions of an object. Here is the problem though, if two rigid designators are identical then they are necessarily identical. Therefore, if Anakin Skywalker is identical with Darth Vader, then he is necessarily identical to Darth Vader. Yet, it seems possible that Anakin Skywalker may have never converted to the darkside. I don't know where to take this question. Darth Vader is a sith, and sith are necessarily converts to the darkside of the force, so that is a necessary property of Darth Vader. Anakin Skywalker does not have the property of necessarily using the darkside, therefore Anakin Skywalker is not identical to Darth Vader. Hence Obi Wan Kenobi was correct when he declared Luke's father and Darth Vader to be two separate persons.