But there is also a nordic surname, and that is known fact.
http://www.sturmunddrang.fi/index.php?page=alexhttp://en.wikipedia.org/wiki/Ann-Marie_Ivars
And, as I mentione before, there is Ívars in Iceland and the Faroese Islands. Plus, HouseOfNames.com account, which says that it was firts found in Normandy, which it's far from the Basque country.
It seems virtually impossible that all these Ivars are of Basque origin.