My first name is Anna-Carin.
Yes, all of that is my first name - it's a compound name just like MaryAnn, LeeAnn, JoAnn, and others. The only difference is that in Sweden these compound names are usually hyphenated. But it seems that they can be hyphenated in other countries too... if you look closely at the logotype of the American Jo-Ann craft stores, you'll notice that Jo-Ann is hyphenated. And it's not just a typeface quirk - at their website you'll see it spelled that way in lots and lots of places.
Anyway, I've noticed that many non-Swedes seem to interpret Anna-Carin as a 1st + 2nd name, and consequently address me as only Anna. That's just the same as calling MaryAnn or Maryann just Mary, or adressing LeeAnn as Lee. Well, maybe people do that too, it's just that I've never seen it done!