Regarding "Brunhild", her name originates most likely from
https://de.wikipedia.org/wiki/Brynhild ...
Thing is, there are various ways to spell that name. It could literally be anything from Brunhild(e) or Brünhild(e) or Brynhildr, if we go with Norse mythology (she's one of the Valkyries). Since we have a lot of more or less modern German names like "Elfriede", "Eckhart", "Zwanziger" and so on, I would say "Brünhilde" is the way to go. But "Brunhild" is technically not wrong either and might work better for English speakers/readers.
Oh, I noticed the discription on Mangadex has her full name as "Brünhilde Rosenmüller Stuckenschmidt"... yeah, that's honestly a mouthful even for German names. Looks legitimate to me, with "Brünhilde" being her given name and "Stuckenschmidt" would usually be considered her family name - but in this case we should probably call it the dynastic name. I'm not sure what to make of Rosenmüller in this context... whatever the author thought, that one wouldn't be used as a given name in German. If ever, you would see it as a family name. My educated guess: she's from the Rosenmüller family line within her dynasty.
But I know nothing about the source material, so take it with a grain of salt.