I think it's pretty clear NeoExDeath was entirely different entity than ExDeath. ExDeath wanted power of the Void, but he certainly never wanted himself to disappear. NeoExDeath is different.
"I am NeoExDeath. All memories... dimensions... existence... All that shall be returned to nothing. Then I too can disappear... Forever!!!"
Doesn't sound like ExDeath at all to me. It's more like the Void absorbed ExDeath and took his power to create a body for itself. That's what I believe anyway.