How would you feel if some random person suddenly changed your name, without your consent or concern? These are fragile minds we are dealing with here. These characters usually have no home, are missing at least one parent, their sibling is evil to some extent, have strange powers that relate somehow to destiny, which effectively adds a substantial weight upon their shoulders, etc...
We would break their little minds if we were to suddenly change their names. An identity crisis would simply be too much, I fear.