Dh and I discussed this before she was born. We knew this would happen. But we wanted to name her after my mother and just figured that we'd all just deal with the name. I myself have a name that causes problems here, so I knew how frustrating it would be. But now that we're actually dealing with it, I wish we'd changed Kathleen into something easier to pronounce like Catalina. It's too late to change it, as Italian law only allows name changes if the name is embarrassing.
Dd is only about a year old now. It will be interesting to see what she wants to be called when she's older, and what she calls herself. I often call her Kathy, which dh's family repeats as Cati. That doesn't bother me too much. I wonder if that's what she'll prefer. In the end, it will be her choice. I do hope she preserves the "th," though, and as she grows I will emphasize that she has a very special name because it's different and because it was her grandmother's name.
BTW, I love your daughter's name!