Jesus Christ, your parents fucking cried because someone accidentally called you by a different name? And you were "horrified" and "humiliated" because someone accidentally called you by a different name? It sounds like you've got no fucking clue what it really means to be horrified and humiliated, because if that's the worst of your problems you've lived a charmed life.
No power level here, I promise, but my name is easy to mispronounce, and also sounds fairly close to a number of other names (fake example: Jerry can sound like Terry), and I literally can't count the number of times people have called me by a different name. My response? I don't give a shit, and I rarely even bother to correct them (I had one elderly neighbor who kept forgetting my name and calling me some random name from his deep past, and I just rolled with it). Hell, my great grandma kept forgetting which great grandkid I was, and it never bothered me in the least. Oh, and that doesn't even include all the myriad of people who have misspelled my name, which frankly happens more often than not.
TL;DR she needs to get a fucking life.