Is kratos the "God of War"?

So after the huge announcement we had recently, there's been a lot of comments about the game being called God of War despite not having Kratos as the main character, him being known commonly as "Kratos, the god of war".
So I read back in the day that the game was called like this because of the events that occur in God of War 1 and I thought "alright, makes sense. God of war because you go kill Ares, the god of war" and since then I always believed that.

But I see a lot of people arguing that Kratos became the god of war and that's why the game is called in such way

So despite the new game and the title and all of that, it got my curiosity. Is kratos the God of War?