Assuming the existence of an immortal being with almost instant regeneration, if he suffered brain damage and regenerated, his memories, personality, etc. would they be restored or lost? Would it depend on the most affected area? And if a specific area was the most affected, could that trigger a chain effect that would also change the rest?
It would depend on the mechanism of the immortality, the speed of the regeneration, and the nature of the damage.
If your being is "immortal" by having something like X-Men's Wolverine's regeneration then, well, the movies depict that quite clearly. Massive brain trauma will cause memory loss as the tissue storing the memory is destroyed, but not personality change other than the small change in worldview due to different memories, as the structure of the brain is exactly replaced. Note however that while Wolverine is very healable and apparently unageing, he is by no means immortal. Destroy his cells utterly, and he is gone.
A TRUE immortal being would need to be able to recover from complete celular destruction. Thus there has to be a mechanism better than mere "superfast organic healing" at work, its healing faculty needs to be able to either ignore damage or retrieve the information of how to rebuild the cells ab initio and ex nihilo. There is absolutely no reason this miracle healing would restore the totality of the cellular brain and not restore the content of that brain at the same time.
I would say it would retain it
Although comics like wolverine suggest it's possible to lose memories, I would suggest otherwise. The healing shows that the body heals exactly like it was before. for example, cells return to their original position as well as shape. Interestingly you can destroy his whole body, but he still retains most memories then, or things like how to walk, write and speak. Comics are very inconsistent.
Memory is retained in two ways. The first way is neural pathways. We learn something, so the neurons make a certain connection. By experiencing or learning something more often, you strengthen the pathways. This can be seen by stronger connections with myelin sheaths around the neurons for example. The connections it makes is the shape of the cell.
The second way is via patterns, which also can be divided in two parts. The nerves can give different signals with the electric signals, not unlike yet different from Morse code. The other one is the patterns of the cells that light up. Your visual cortex is constantly alight with activity. Many things will trigger similar responses in the cortex. Yet they are viewed differently. As an example, you recognise a lot of faces. It activates lots of similar structures, yet a slightly different pattern is active for each person.
The thing is that you can destroy the nerve cells, but if they regrow in the exact same size and shape, they make the same connections. As they would be identical to the last one, they should retain the same patterns for all patterns. Depending on your idea of healing, the size of the damage shouldn't matter.
The truly interesting thing here is that healing suggests reverting back to a previous state, yet memory or even just getting hungry suggests a different state. Memory means making and destroying connections. Why wouldn't that 'heal'?