I can think of some reasons why we use Die Queen
in German, but refer to Königin Beatrix der Niederlande
.
Most people in Germany understand a fair amount of English, at least in ex-west-Germany. We say President Obama
as well, for example.
We had a time of occupation were the English language could greatly influence our own, and there is the British national anthem God save the Queen
that is, at least for its title, known to some degree in Germany.
So yeah, if you talk about Die Queen
in Germany, you are talking about Elizabeth.