First, a correction to a point you made. The abbreviated (G-xx) format is only used after you are addressed that way by the ground station. If the ground station continue to use your full call-sign, then you must use your full call sign when replying to them. (In practice, it's so rare that they need you to use your full call sign that when they do, they'll always explicitly say something like "G-ABCD, use full call-sign please, similar call-sign on frequency." And after you confirm that, they'll tell the other guy too: "G-YZCD, use full call-sign please, similar call-sign on frequency.")
As for other call-signs, they are allocated by the international radio licensing organisation (whose name escapes me, but it's one of those alphabet-soup acronyms). Anyone can apply for one. Certain schools use them - one particular school I know of has one for each of its instructors, and another one for each of its aircraft when there's no instructor in the aircraft. But you have to apply for, and be given, permission - you can't just start using a call-sign because you think it sounds good.
Hope that helps!
FFF
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