Here's an amusing, possible scenario. I suppose I could write it as a fanfic, but for now it's just an amusement.
Her parents, Onald and Martha, happened to deliver Brunhilde at a hospital in America where, like most Americans, the person running the records system had no notion of how to enter a ü at the computer keyboard, and wouldn't have considered the lack of an umlaut to be a misspelling anyway. So, her birth certificate name is actually Brunhilde. Her parents, again like most Americans, didn't really notice or take seriously that kind of spelling variation, calling her Brünhilde until, aged seven, she came home from school one day after a class in phonics, and announced to her father that they had been mispronouncing her name for her entire life.
Onald, considering this, sees that his daughter is not particularly upset about it, and knows from earlier investigations that attempting to change it will involve, at the very least, some administrative fees, logistical difficulties in their schedules, and probably some tedious standing on queue in some dusty government building somewhere, an activity which he passionately hates. So, forthwith he apologizes to Brunhilde for mispronouncing her name for her first seven years and considers the matter settled.
Martha, when she gets home that evening, is less sanguine about the whole matter, and begins to raise a protest. Then Onald fixes her gaze with a stern eye and explains why he knows what the name change entails. On his own, handwritten, birth certificate, there is an odd squiggle in front of his name. His father had always maintained that it was intended to be a 'D', and his mother had claimed she wanted it to be an 'R', and finally, when recording the birth on their tax forms that year, they had dropped it altogether leaving him with the part of the name that both could agree on. Later in life, at various moments when officials had looked at his actual birth certificate for various reasons, no-one had been confident enough of their reading of the squiggle to put an extra letter in front of his name if he wouldn't tell them what it was, so Onald he had remained....
It is telling that my own computer's spelling dictionary, set to American standard spellings, has placed a red squiggle under 'Brünhilde' above but accepts 'Brunhilde' as perfectly correct.
Short version though; her parents were American, and Americans, having invented typewriters with limited keyboards and later developed them into computers with limited character sets, have been dropping diacritics and accents without a second thought for generations now. Even though modern computers make them available, Americans are simply accustomed to their absence.