Is her name really Nazi or am I reading it wrong?
Nazi (Na-zee) is a common name in the country of Georgia.
I knew a girl with exactly that name, and nickname, back in the 1980s in college. She and her family had fled the takeover by the Ayatollah.
As for relating it to Hitler's Nazi Party, there is no relationship. Just as there is no relationship between the Vietnamese nickname "Phuc" and that most common four letter word on the streets of New York.
She really should change the spelling. Even Nozzie would be better. What a beautiful girl!