As has been mentioned in other answers on SE, it's likely that both Skywalker and Kenobi are common (or at least unremarkable) names on Tatooine, so hiding away was not an issue per se, except for possible rumors that Ben was a Jedi, as stated in the question. However, keep in mind Uncle Owen's attitude towards Ben (obviously to dissuade Luke from getting involved), that he's a "crazy old man." If Uncle Owen has managed to make his opinion more widespread (something which Ben himself would probably encourage, though for different reasons), then it's not really that obvious. The Galaxy probably contains numerous crazy people called Kenobi, perhaps even multiple ones who seem to think that they're Jedi or have magic powers. Even on Tatooine, that probably won't trip any alarms.
[Speculation: maybe someone did try to turn him in, and the stormtrooper patrolman (who could likely be a local recruit) laughed it off with a "he's just a crazy old hermit" comment (again, assuming that Uncle Owen's attitude was common).]
Now, if it became clear that Ben was associated with a Skywalker who lived at the Lars homestead, and this info ever reached someone who would know what that means, obviously there would be problems. But remember that aside from the Larses, Obi-Wan, and Vader himself (and R2-D2), nobody in the Galaxy knows the significance of a Skywalker living at the Lars homestead in relatively close proximity to a local madman called Kenobi. In fact, a Skywalker at the Lars homestead would seem downright natural, given that Lars the Elder used to be married to the Skywalker woman who was offed by the Tuskens; the connection to a Kenobi would probably be missed, given that Obi-Wan wasn't involved in the events on Tatooine in Ep.2 and stayed on the ship in Ep.1. So the situation wouldn't be suspicious to anyone who hasn't seen the Star Wars movies, and Kenobi is a tolerated local kook. Anyone trying to turn "old Ben Kenobi who thinks he's a Jedi" in as a genuine Jedi probably wouldn't be believed, if anyone even bothered to try.
EDIT: I've edited some of the wording above to reflect the tentative nature of these statements in the absence of a better source than other answers on SE. Keeping it around in case I find more/better sources.