Is there a female version of the Old Norse name Einar?
I’ll point out that the name Einar is believed to be derived from the einherjar, undead warriors in Valhalla. It’s very masculine in origin and I wouldn’t be surprised if there isn’t a female version. That said, I’m speculating and could be wrong.
If I had to guess I’d say Eina. I went to school with an Ina.
Eina would seem to be the female equivalent:
Your own cite would indicate it is Einara as well.
There’s no Old Norse female version.
As for Einara and Eina: There is no one registered with the Einara version in Norway today, or in the 1801 census, although there were 15 in the 1900 census. It’s only a female version in the sense that any Scandinavian male name could be feminized by tacking an a at the end in certain times and places.
And Eina is similar. None in 1800, 5 male, 7 female in 1900, 23 today, all female. I think the Nordic names-site is wrong in stating it’s a female name of Einar though. It’s entirely possible that’s the origin, but it might also be a local spelling variation of some other name. Online Name-databases are notoriously weak on checking their etymologies.