Those who were enrolled at the Imperial Academies were called cadets. The term was also used before then, during the time of the Galactic Republic, for the same purpose when clone troopers were being trained. The main facility where many of these cadets were trained at were academies such as the Academy of Carida, where many famous stormtroopers have been trained.
A similar rank, called "recruit," was utilized by the Alliance to Restore the Republic post-Battle of Hoth, being the lowest rank, just below Flight Cadet. Its insignia was a white patch with white borders and completely bare.