EDIT: I just thought of my own answer. At the time that was re-edited back into the SEs, George probably hadn't decided whether or not Vader was supposed to be well-known as the same person as Anakin Skywalker... even though no one seems to know it at any point in the OT. But going back further, when that scene was written and filmed, Vader and Anakin probably weren't the same person at all. Trying to think like Lucas makes my head hurt.
EDIT: I just thought of my own answer. At the time that was re-edited back into the SEs, George probably hadn't decided whether or not Vader was supposed to be well-known as the same person as Anakin Skywalker... even though no one seems to know it at any point in the OT. But going back further, when that scene was written and filmed, Vader and Anakin probably weren't the same person at all. Trying to think like Lucas makes my head hurt.