The Prequel Trilogy.
All through Phantom, Clones and Sith he is referred to, and only referred to, as Obi-Wan Kenobi. Never as Ben.
By the time of A New Hope he is known to Luke as Ben. This makes sense. To Luke, the gang at Toschi Station and anyone in or near the Homestead he's just a "Crazy old wizard." Owen, to protect Luke from his father, has tried to keep Kenobi away, and Kenobi for his part plays into that role, all the while keeping a watchful eye over young Luke's development.
So, to native Tatooinians he would be known as Ben Kenobi. Fair enough.
It makes sense to assume that the name Ben was created by Kenobi himself to deflect attention away from the fact that a hero of the Republic and one of the great Jedi is living just a few kilometers away from the son of the Chosen One on the planet where Anakin Skywalker himself was raised.
And therefore, the reason why he was never referred to as Ben during the time of the Prequels.
Given that, it still makes one wonder why Luke continued to go by the name Skywalker, risking detection by carrying a surname that was notorious throughout the galaxy...