The Jedi and the Sith are not very sleuthy, are they?
How many years does Yoda have council meetings in the same room as Palpatine, none the wiser?
Luke Skywalker was raised by his aunt and uncle. He had the name Skywalker, but his uncle had the name Owen and his aunt's maiden name was Whitesun. How does that not raise a red flag? And Obi-Wan is just living on the other side of the hill?
Maybe the Emperor knew he would attempt to enroll in the academy, and would then turn him to their side without a fight.