Rad, Alicia, and Lavian are generic characters though. Their appearance changes when they change jobs just like any other soldier you can recruit. They have no unique skills like Guts or Mighty Sword. Their names stay the same simply because they're involved with the main plot, albeit in only one scene.

You can keep them if you like, but it'll make breeding monsters more difficult. Just try to do as much breeding as you can before you fill up your ranks with the likes of Cloud and Worker 8. You can breed almost any class before Nelveska Temple except for Hydras.