After Revenge of the Sith, it is assumed that Kenobi leaves Anakin to die. Kenobi had no idea that the Emperor came to save Anakin. He also hid Luke and Leia to keep them from the Emperor, not Vader. So it’s completely plausible that Kenobi didn’t know Anakin was Vader. Now Anakin became Darth Vader before he was disfigured, but I don’t think Obi-Wan knew he was Darth Vader. I don’t have a problem with what the writer said. It’s consistent with Obi-Wan not knowing that Anakin survived.
Perhaps that's a plausible argument, but as soon as he would have heard the name "Vader", he would have instantly known he was indeed alive - and later dialog indicates he knew he had survived even before that.
He also hid Luke and Leia to keep them from the Emperor, not Vader.
"To protect you from the Emperor, you were hidden from your father..."
So it’s completely plausible that Kenobi didn’t know Anakin was Vader. Now Anakin became Darth Vader before he was disfigured, but I don’t think Obi-Wan knew he was Darth Vader.