As noted in this question (similar, but not duplicate), Obi-Wan did know that Anakin was not dead, and that he was, in fact, Darth Vader. In this question, it is clear that the fact that Anakin was Darth Vader was not common knowledge at all.
So when how did Obi-Wan know Anakin had become Darth Vader? I don't recall reading any EU novels with any interaction between them.
Did he know at the time of their duel on Mustafar that Anakin was called 'Darth Vader'? If so, then he simply would have heard about Vader in other events and this is a dumb question