John Doom raises a very good point.
In fact, although Vader says in ESB that he is Luke's father, never once does he say "I am Anakin Skywalker."
Even Yoda is careful to refer to Vader as "Obi-Wan's apprentice."
The definite assumption that Darth Vader and Anakin Skywalker are one and the same person actually appears to date to the writing of ROTJ, not ESB.
After all, it's quite possible that Mother Skywalker was getting some action on the side....