Alex had inherited the memories of the previous Undying Gods. The memories were fractured and were just that, memories.
They didn't give any insight into their being or their true personality. Alex was only affected by what he saw through the eyes of the person who was once an Undying God.
The memories weren't impactful, but they did feel like his own as if he lived through them. Perhaps only the first memory of the first Undying god was where he truly felt the emotions and despair of the person he thought he was.
Having so many memories at once did make it hard for him to keep a stable mind as to who he was.
Fortunately, he was killed multiple times before he was passed the inheritance too.
As the 6th Undying God devised, killing someone over and over was a good way to strengthen one's will and understanding of who they were.
