Non-EU PhD title in Germany

I am a German PhD student in South America and am worried about whether my PhD title will be accepted in Germany (as Dr.) and internationally in general.

If you successfully complete a PhD in the EU, you are allowed to carry the title "Dr.", as any PhD in Germany does.

I am working in a faculty with a professor with international experience, who, for research reasons, left a reasonably strong department in Europe for the position in South America, which is incidentally one of the strongest two departments in South America.

I am attending international conferences every now and then, have two papers published in international journals (one jointly, one alone) and two more papers in preparation.

For all I know, I can reasonably expect that my research performance (and eventually, my PhD thesis) is not below the European standard.

The default format for PhDs from a non-EU country is something like "Hans Wurst (Doutorado, Universidade de Ipanema)", which looks like I should just use my self-confidence instead and not mention that I did a PhD unless someone asks.

I don't know if it's off-topic, because this might just be "too localized", but of course I am wondering if it is possible to have my PhD accredited to use my PhD title in Germany like any "normal" PhD.

I'm also wondering, whether the international community is as strict as German law, or whether I should just call myself "Hans Wurst, PhD" on job applications, my professional webpage, etc. (where the place will be listed somewhere), and hope nobody tells me it should be "Hans Wurst (Doutorado, Universidade de Ipanema)" instead.

Did I make a mistake in my career planning in that the only title that is worth carrying (until full tenure, I guess) I can't carry without a large number of not-so-fancy accessories?