A Quick Overview Of How To Say Sigrun
Sigrun is a Valkyrie in Norse mythology which is written in Old Norse - a Germanic language. Her name here is traditionally written with an accent on the ú, which could imply that the stress falls on the second syllable, which was my initial thought.
I consulted Dan McCoy from norse-mythology.org about the pronunciation and where the stress falls, and his view is that the accent probably does not indicate stress, and the more likely pronunciation is SEE/groon, but of course, as with all ancient languages nothing is certain. I'm going to suggest you follow option 2 on the audio as being the more likely pronunciation, unless anyone else wants to weigh in with a compelling argument to the contrary.
What I don't know is whether the accent on the 'ú' changes the vowel sound in another way - it may well do, but again we are speculating because there is no-one alive to give a definitive answer.
Sigrun is also a fictional member of the Legion of the Dead.