"insert name of third generation German-American here"
I must admit to being puzzled by the number of times I hear Americans refer to that sort of thing. Are they all ghettoised and stick with "their own"? Surely by the 3rd generation they are likely be even more mongrelised than their immigrant forebears in terms of mixed heritage.
One set of great grand parents were Irish. Another set were English but of French descent. Does that make me Irish-English, French-English or, as I prefer, just English (or British, or European (for now) as I choose)