Can you get brain damage from lack of oxygen from snoring?

2 different events. Snoring results from vibration emitted from the upper airways, for instance a sides of the nostrils moving toward the septum during inhalation or more likely from vibration of the soft palate, uvula & perhaps tongue. Snoring is a noise. Its cause is airway obstruction. Severe obstruction blocks oxygen getting into the lung, hence possible brain injury--consider having polysomnogram test.
Snoring Brain Damage. Generally, even excessive snoring will not cause "brain damage". However, if oxygen levels drop during sleep, and this can come from snoring when breathing stops, a condition call sleep apnea, brain function may be affected. Memory loss, feeling "foggy", and irritability may all be associated with poor sleep quality from severe snoring, with sleep apnea. Go see your doctor - request a sleep study.