Toblach is the German name, Dobbiaco the Italian one. When South Tyrol fell to Italy, many places had no Italian name at all. They were deep in exclusively German-speaking territory. Names had to be invented.
Many a bomb has been thrown about those matters 60 years ago, but, by all means, things have been resolved. They always do. It’s Europe. There’s not even a border. There is a sign telling you that you leave Austria, and there’s another sign welcoming you to Italy. That’s it. Everybody makes business with everyone. Just like it should be.