Passports normally don't have information about what country you live in, that is where you are a resident. Passports show which country you are a citizen of. 

The country were you live is your country of residence. If you are a resident of another country than where you are a citizen you need a proof of residency.

The country of residence only matters if you live in Europe and use Interrail, as you only can travel on a maximum of 2 travel days in your CoR.

If you live overseas and use Eurail your possibility to travel is the same no matter what CoR you have.

Thanks! But in my german passport there is a Field with Residence with Zurich. So would I have to prove that I am a resident of Germany?

If you have a German passport that suggests you have residence in Switzerland I would ask where you physically live - i.e. your main address where you have your mail sent. Irrespective of your passport that is what matters. If you live in Zurich then you declare Switzerland and can only use your pass in Switzerland on a maximum of 2 travel days.

If you now live in Germany your Country of Residence is Germany and again you would be limited to 2 days travel in Germany. 

Remember that a train inspector has a duty to prevent residents of his home country using a train more than 2 days on any pass, If you choose Switzerland I doubt a German inspector would accept your passport alone as proof of residency as it may be out of date (i.e. you may have been living in Zurich at time of issue but moved back) so take something recent with your address.

On the other hand.If you choose Germany as your COR it is unlikely that a Swiss inspector would not accept a German passport for unlimited travel in Switzerland.