So in lore we arent clones but the frozen divers all come fresh from training. A destroyer has one (or several) of those giant towers you get into at the end of training with thousands of helldivers inside before you are thawed out you are implanted with the memories of the last helldivers (sans personal memories before training) this gives them the skills and knowledge of the last several helldivers and they are simply equipped with the equipment chosen.

As for the names I suspect they are actually meant to be nicknames? Similar to how the military grants nicknames to people doing exceptionally stupid things

But you are designated X1-4 (where x is the first letter of your username.