Ethnic self-identification is a pretty cool aspect of studying census records, actually. The actual evolution of the census (especially in the last few decades) to reflect the diversity of what people call themselves is the subject of countless sociological journal articles, to be sure. But that's my inner nerd talking.
As for me, I grew up in the US and have two passports (with a couple more passports on the way). I don't do hyphens. Our kids (as ktspktsp and I are often joking) are going to be ThaiceLebandic.
And I don't give a flipping fuck what anyone thinks about that. If you're taking it too seriously, then that's your problem.
Exogamy is the way to go, a la Crompsin's post.