At least en français you get it easier - just use "Duc de Daman, Diu, et Nagar Haveli" or "Duc de Daman" for short. In other words, a translation of the (Canadian) English.
But the two bits were "Daman and Diu/Damão e Diu" and"Dadrá e Nagar-Aveli", so wouldn't the combined name be the two first bits, namely "Daman and Dadra/Damão e Dadrá" ??
If Nagar Haveli is the more important portion of the second possession, then why is it second in the title.
I'm not saying you're wrong, I'm saying I don't understand.
Edit: besides, isn't Daman and Dadra more alliterative and nice sounding? Of course, I have no clue what sounds better em Português