At the baseball game, Cooper mentions that when he was younger, everyone was too busy fighting over food to be playing baseball.
The implication is, society had almost totally collapsed. Things like centralized records would no longer be maintained. As zack said in comments, NASA had no idea if Cooper was still alive let alone where he was.
In addition, we don't see much evidence of computerized records or the Internet in Cooper's community. As I recall, the school office is full of paper files instead of computer terminals. Cooper is considered pretty weird and eccentric for building computer-controlled farm equipment. Whatever government still exists may be rather decentralized and keep its records on paper, so searching for any records of Cooper would be a difficult and possibly futile task.
Finally, the general public are not aware of NASA's continued existence. NASA are trying to keep a low profile, and wouldn't want to draw attention to themselves by actively searching for Cooper -- especially since their resources and personnel are very limited.
Bearing this in mind, it's a remarkable coincidence that of all the places Cooper could have gone,
he lives less than a day's drive from NASA's secret headquarters.
We can just call this dramatic licence, unless there was
additional interference from the black hole engineers
which doesn't really seem consistent with
their need to recruit Cooper to communicate with Earth in the first place.