Welcome to HCM.
You have been diagnosed with Naevus depigmentosus to which you are not satisfied. For the diagnosis made by doctor you might be correct in two senses. One is It doesn't generally appear in Adult life and then does not increase in size to involve all over the back.
Though you should also understand that we may find so many diversities in any clinical problem and the doctor has devised a right approach to diagnose your condition with best of his/her clinical knowledge. The doctor might be true in your case as considering segmental or systematized forms of Naevus depigmentosus.
The best possibilities if especially vitiligo
is ruled out remains to be Post Inflammatory Hypopigmentation
(PIH)- In this condition any of skin rash
or infection which heals either leaves hypo pigmentation (lighter color than rest of normal skin). Back is such area which is not accessible to visualize by the individual herself or himself so anything occurring at this place is not noticed in early phase. you might have had some sort of same problem and is noticed at the time of hypopigmentation.
Any how you should understand that both the above conditions are totally benign (simple things) so you should not be worried about the same.
But Yes if the hypopigmentation ( in your language whiteness ) increases or spreads to other parts of body then you must must take second opinion
from a Senior Dermatologist
Hope to give you a point of satisfaction and best wishes of health