Imagine the number of ways things could've gone wrong. Luke could've sent his application to the (Imperial?) Academy, prompting a background check. He might've mentioned "crazy Old Kenobi" in a letter to his friend Biggs (an Imperial officer according to most EU sources), catching the attention of Imperial Intelligence. His friends in the Mos Eisley cantina might've turned him in (well, they did, eventually). The local constabulary might've decided to look at Imperial warrants, so they didn't appear completely useless. Jabba could've heard that there's a Kenobi on his planet, and make the connection -- Jabba could've sold him to the Imperials, or probably even taken him himself.
Contrary to popular belief, the best way to keep a secret is not to "hide it in plain sight." It's not to tell anyone. Obi-wan Kenobi failed on this point.