Has anyone died from brain freeze?

There are no documented cases of anyone dying from brain freeze, also known as ice-cream headache or cold-shock headache. Brain freeze is a common and generally harmless phenomenon that occurs when something cold touches the roof of the mouth (palate), causing a sudden and temporary headache. This sensation is caused by the rapid constriction and subsequent dilation of the blood vessels in the palate and can be quite painful, but usually goes away within a few seconds to a minute. Brain freeze can be uncomfortable but is not life threatening.

brain freeze can't cause brain damage. That pain is either caused by stimulation of the trigeminal nerve in the roof of your mouth or by cold air in your sinuses resulting in an abrupt contraction of the blood vessels in your forehead (similar to the way migraines are caused). Either way, it's fleeting, superficial and isn't actually cooling the brain to any appreciable degree.

https://www.sciencefocus.com/the-human-body/can-brain-freeze-cause-brain-damage
https://en.wikipedia.org/wiki/Cold-stimulus_headache