Calling himself the demon lord is an extremely stupid choice for the exact reasons that Noah brought up. It makes him an enemy of BOTH the real/new hero (who goes to fight the demon lord) and the real/existing demon lord (who would be upset at the seeming challenge to the throne). He could've just declared himself an extremely powerful person. He could've declared himself monster tamer. It doesn't matter. Almost any other choice would've been better.
But wait, doesn't that make him look more powerful and potentially ward off attacks? You mean that his already shown power to the two S rank adventurers as well as the reports to the governments wouldn't already be enough to ward off the attacks? If that's not enough to ward it off, then calling himself the demon lord wouldn't be enough, as literally evidenced here where they are mobilizing in order to fight the demon lord. It just makes everything worse.
And I'm still really unsettled by the mind-broken, brainwashed slave who's only happy because he's mind-broken and brainwashed.