I should add that in the most formal settings in the German-speaking world someone with two Ph.D.s will still be introduced as "Doctor Doctor." If a man also was a professor he'd be "Herr Doctor Doctor Professor."
Getting uptight about such formalities is, in my experience, mostly a North American thing.
I remember some years ago requesting a written professional recommendation from an English gentleman, highly accomplished in his field.
The letter was intended for a Continental audience, so he signed it "Herr Professor Doktor Doktor xxx".
He showed it to me, winked, and said archly, "they love this kind of stuff."