After a quick skim

        "This sword," he said, "is one of three made by Ivaldi the
Ancient, most legendary smith in all the Heavens, for the three sons of
Borr: Odin, Vili, and Ve.  This one belonged to Vili the Strong until
his death aeons ago in the Great Battle of Vallgatr.  Since then she has
passed through many hands and been known by many names.

It does have a name, in fact it has MANY names. Its just that they're all not germain to the story... yet.