Actually no, he was always Death, even in The Sin War LONG before the games he was referred to as Death, he just started calling himself Wisdom one day and everyone went with it. It seems that Angels sometimes don't realise their own natures (for example, Imperius calls himself Valor, but is really Wrath/Justice (since he's always been crazy about rules and flies off the handle when someone goes against them), Tyrael called himself Justice but was really Wisdom all along (after all, he may have acted as justice, but he always used methods of judging that are more wisdom-based (like the fact that he acknowledges that his initial judgements of humanity are wrong when he gets more information))

And he didn't exactly decide"humans need to die or we're all screwed", his logic was "angels and demons don't get to choose between good and evil, and we're IMMORTAL, these brief things can't comprehend just how far reaching the consequences of their actions can be, they DEFINITELY shouldn't be able to choose evil!"and he went NUTS after the world stone got destroyed, so I wouldn't exactly call the acts of a madman "wisdom"