Is the white patches after peeled sunburn permanent?

Typically no: When sunburns peel, the underlying skin has not had much uv exposure so it is usually much more pale than surface sun exposed skin. It is important to use metallic based sunscreens including zinc and titanium to block uva and uvb rays so that safe re pigmentation will occur. Pale skin is at higher risk for recurrent burns which is the primary cause for skin cancers. Avoid those burns.