You cannot be Turk and German at the same time. You cannot be Greek and Italian at the same time.. you can live in both states and have a passport and be officialy a member of both states, sure. But it's hard to say that youre a turkish German or a german Turk.
What you mean by half turkish probably means those young people that were born in Germany as children of turkish immigrants that came to Germany during the last fifty years. They probably call themselves German and Turkish due to their roots and connection to both countries.
Imo you should decide. ^^ It is hard to say that youre turk and german at the same time, there's so much difference. Not only religions, culture and stuff.
Of course we are happy in Germany that so many people came here, and not only Turks after all.