I know you have done posts about the etymology of the name Sigyn, but what I was wondering was if you might know where the idea that she's a Valkyrie comes from? I see a lot of posts on here saying that her name means friend of victory and that means she was a badass Valkyrie serving Odin, which doesn't make any sense or seem likely to me. I honestly feel this way because of stanza 22 of Lokasenna, wherein Loki calls out Odin's treatment of humans in battle, which makes me question why he would marry a Valkyrie. I don't know, maybe someone else can answer this, if not. I'm going to write a post about my continued quest to find more fun books about Norse mythology and Loki especially, so I will most likely mention it in that.
I agree with you that the theory that Sigyn is a valkyrie is not correct. I'm not sure where it originated, but there are a few reasons that I am not surprised that people believe it.
Sigyn has been studied and debated for well over a hundred years, but nobody really proposed a good etymology for her name until 2017, and he did it in a very dense linguistics paper that's difficult for most people to understand. Especially in his second, more verbose paper on the subject, he also included a lot of comparative Indo-European mythology that most people rightly regard as speculative and outdated, and while it doesn't ruin his etymological argument, some non-linguists might object to it and find the author less credible because of it.
The element sig- or sigr- means 'victory' and is very common in Old Norse names in general, and occurs twice in Valkyrie names (Sigrdrífa and Sigrún). It's much more common in human names, but Sigrdrífa is an important enough figure to stand out and probably adds to the perception that sig- names are typical of valkyries.
We are now fairly certain that Sigyn's name is actually Sígyn with a long i, so it isn't 'victory' at all, and most likely originally meant something to do with pouring liquid, but again, this was only formally demonstrated in 2017 in a paper that few people have read. So the 'victory' interpretation prevails for now. It had a 100+ year head start, and it will take a long time for Ginevra's new etymology to reach people.
Since deity names usually have some connection to the deity's role, domain, or actions they perform in myth, it seemed for a long time like there was an unanswered question about what exactly Sigyn did that was victorious enough to be named that. Deciding that she must be a valkyrie is a neat solution to that question, because it would mean she doesn't have to acquire victory herself, but because valkyries pertain to granting or withholding victory in general it would make sense for a valkyrie to have that name.
The last thing that I can think of is that it could be an extension to a theory about why Loki is hanging around with the æsir to begin with. It's a common theory that Loki's mother Laufey was an áss and that's why he took her name as a matronymic rather than his jötunn father's. But it also makes some sense to propose that he married into the æsir. It's enough to suggest that Sigyn is an áss, but to say that she is a valkyrie ties up the previous two points and connects it to this one, because valkyries pertain to the æsir through Óðinn, even without really being æsir themselves.
So basically, it's a nice, neat theory that cleanly ties up a lot of loose ends, it's just that whenever you find one of those in the field of Norse mythology it's almost always wrong.
[Edit] I should also add that I understand that for some people this is really more of a gut feeling interpretation and that many people have found meaning in the 'victory-friend(fem.)' interpretation even while understanding that it isn't etymological, I'm really not trying to dismantle any of that, but just to clarify what's represented directly in medieval texts.
