Why objects are uniquely defined by their right ascention and declination?
Stars do not change their right ascension or declination values as the 
Earth turns. 

The position of the stars in the night sky (called azimuth and 
elevation) will change, but that's because the lines of right 
ascension also move. 

However, right ascension and declination do not uniquely define an 
object. Over time, stars move with respect to the sun (called "proper 
motion"), and the direction of the Earth's north pole (currently 
pointing near Polaris, the North Star) also changes (called 
"precession").