This would allow for Ben to be Kenobi's birth name and 'Obi-Wan' to be the name he took when he became a Jedi Knight. When he reteats to Tatooine, with the infant Luke, he reverts to his birth name of Ben Kenobi. This is not a clever subterfuge to avoid discovery. It is sufficient that he came to a world so unimportant, in galactic terms. I feel that it is clear, from Vader's line: "I've been waiting for you, Obi-Wan", that the Sith felt that the Jedi were no longer able to oppose them, having been decimated and scattered by the purges. They did not feel the need to obsessively pursue every last member of the order. They knew, as the remaining Jedi would have known, that if any of them showed themselves, the Sith and the Empire would come down upon them swiftly.
This would allow for Ben to be Kenobi's birth name and 'Obi-Wan' to be the name he took when he became a Jedi Knight. When he reteats to Tatooine, with the infant Luke, he reverts to his birth name of Ben Kenobi. This is not a clever subterfuge to avoid discovery. It is sufficient that he came to a world so unimportant, in galactic terms. I feel that it is clear, from Vader's line: "I've been waiting for you, Obi-Wan", that the Sith felt that the Jedi were no longer able to oppose them, having been decimated and scattered by the purges. They did not feel the need to obsessively pursue every last member of the order. They knew, as the remaining Jedi would have known, that if any of them showed themselves, the Sith and the Empire would come down upon them swiftly.