The only difference between the alternators(that fit any given engine)would be the max charging current (amps). And because the cars with V8 will most probably be fully loaded there are no 4 alternators available for the V8. As a matter of fact if you open Realoem you may find that there are 2 alternators available for your model - 180A and 220A. Even if you put the other type than the one you have it will not burn anything and it will not burn the alternator itself. Regardless of how complicated it all looks like, the basics are the same.
Not registering the battery in the car will not cause a not charging condition in any case.