How did the public see Darth Vader

What did the public know about Darth Vader?

Understand that between the time Anakin pledged his life to Darth Sidious and when he reappeared in public as Darth Vader behind the mask and suit, very few people see and live him. The Jedi in the temple will be wiped out. The seperatist leaders will be exterminated. The only ones I can think of who saw Anakin between his fall and metamorphosis and who are not shown dead by the end of Ep III are Obi-Wan, Palpatine's personal guard, and some clone troops. The latter two categories can be dispensed with if necessary. The medical droids that worked on it can easily reset their memories. Yoda knows what happened to Anakin, but only sees Anakin in a taped security hologram that is exterminating the Jedi and the boys in the temple.

Also, remember that the people who care most about the secret of Vader's past are the Jedi, not the Empire. Luke can't know Vader was Anakin until he's ready to know. Luke used the Skywalker name when he was growing up. At least on Tattoine, that's not incredibly dangerous, as Shmi Skywalker was known as Cleeg Lars' wife and before that as a slave. Who knows who Watto hooked you up with to pay or buy someone off? But if he had heard or grown up and known that Vader's real name is Anakin Skywalker, one of two things would happen; he would either reject power altogether and know what it did to his father, or he would see his father before he was ready. Frankly, as naive as he was, he might have started asking questions about the Skywalker name that would find their way back to the Emperor, which put Luke in serious danger long before he ever bonded with the rebels.

In contrast, it's just a little practical that Vader's backstory in the universe isn't more public. If the galaxy knew that one of the most feared characters to the Emperor's right was Anakin Skywalker, formerly one of the most powerful Jedi in the galaxy, it would only add to the fear for Vader. If people don't know that he is human himself, it can be useful for the same purpose, so it's just never mentioned.