Anakin made the transition to Darth Vader almost immediately after his part in Mace Windu's death.
Remember guys, Papa Palpatine says to Anakin while he was kneeling "Henceforth you shall be known as Darth Vader"
DV says "Thank you, my Master"
Papa P "Rise"
From that point on he is Darth Vader. I think that we've begun referencing 'Fallen Anakin' just as a way to differentiate Darth Vader with and without his suit. So essentially it's not the suit that makes Vader moreso than his characters personal schism. My friends and I just call him Zero Suit Vader when we're talking about that.