I believe that there's no real explanation for this thing. We can only assume about the details.

Though presumably, Dumbledore realized that this curse existed after several teachers came and went. Well, if you're a headmaster of a school and you've been on the job for years, I think you'll indeed notice if such a hiring problem exists, and with one job at that.

And with Dumbledore being Dumbledore, we can assume that he eventually realized that it's highly likely that Tom Riddle was the one who placed the curse. As presumably, the curse appeared after he was refused the DADA job when he asked for it.

>"You see, we have not been able to keep a Defence Against the Dark Arts professor for more than a year since I refused the post to Lord Voldemort."
—Albus Dumbledore

We don't know if Dumbledore already did this renaming thing. Though it's kinda obvious that Dumbledore never did figure out how Tom did the curse. Or else, he would have broken it already.

>This jinx was cast by Tom Marvolo Riddle, who was by the time known exclusively as Lord Voldemort, to curse the Hogwarts school's Defence Against the Dark Arts class to ensure that none of its applicants could hold their post for more than one year. It is unknown what the requirements and incantation of this jinx are, or if it could be used for other school subjects or other establishments and careers. The jinx will be lifted once the caster is dead

from http://harrypotter.wikia.com/wiki/Voldemort's_Jinx_on_the_post_of_Defence_Against_the_Dark_Arts_teacher