I have the same issues with my kids names and family. I know we didn't make it better by naming our ds a name VERY similar to my nephew's name. Dh still gets mixed up too. Our names are Arabic and I really didn't want to name them something that would cause others to mispronounce because a slight mispronunciation could drastically change the meaning of the name to something with a different and/or bad meaning. We wanted to name our first dd Sahlah, with the 'h' pronounced, but the American 'tongue' makes it sound like Saklah. I ran it by the inlaws and on the first try, I knew it wasn't going to work, lol. So we switched to the other we were going to choose, but they STILL mispronounce it and I admit that I don't correct because in general, they tend to have trouble pronouncing some English words, so I digress.
In a nutshell, I'd say encourage your dd to be proud of her name AND its correct pronunciation. Changing it to an Americanized pronunciation just dilutes its specialness. I like the name and really don't think it's THAT hard to pronounce. It's not like its some strange letters completely foreign to English like some Arabic words are.
Anytime some teacher, nurse, caller on the phone, etc. mispronounces it, encourage her to correct it. My mom never really told me this at your dds age. I know I didn't as a child and I still get mad when I remember how my second grade teacher mispronounced my name for a long time until my mom came up to the school and noticed it. When my mom told her, my teacher was surprised I didn't say anything. I was shy about correcting an adult and still was when it happened again when I was 17 y/o! It wasn't until I felt like an adult (sometime after graduation), I started standing up for my name and its correct pronunciation and meaning (the mispronunciation DID change its meaning).
One more thing is that nipping it in the bud early helps stop the spread of incorrect pronunciations. With my experience, I realized that when people heard others pronouncing my name wrong, others would just repeat it who've never me before and didn't ask me what my name was. Even people who did know my name's correct pronunciation and had known me for many years started pronouncing it the wrong way w/o even asking me first. I guess they thought the 'new' way must be the right way and were too embarrassed to ask themselves!