Anakin will become Vader before the fight
As turmoil engulfed the galaxy during the transition from Republic to Empire, Anakin fell to the dark side of the Force. Consumed by evil, Anakin abandoned his past and his humanity. He became Darth Vader, Dark Lord of the Sith, apprentice to the evil Emperor Palpatine.
Sustaining grievous injuries at the hands of his former master, Obi-Wan Kenobi, Vader required cybernetic enhancements and replacements to sustain him. His pure innocent self seemingly lost forever, Darth Vader cast a dark pall over the galaxy, as he was one of the foremost agents responsible for the elimination of the Jedi order. (SW.com)
Reading this I take it as Anakin becomes Dark Vader by name early in the movie and after the fight Vader then becomes the Vader in the mask. Which also tells me that Vader with out the mask will be responsible for the elimination of the Jedi. That reason why Obi-Wan new that Anakin was Vader with and with out the Mask.