Basque pronunciation is similar to Spanish so, knowing that, we know that Edurne is pronounced either "eh-DOOR-neh" or "eh-DUR-neh".Several Basque dialects also have no obvious stress on syllables so Edurne can also be pronounced simple "eh-door-neh" or "eh-dur-neh".
Like Ora said, ed-UR-na, eh-DUR-na or eh-DURN-eh would be the pronunciation. But, from the way it's spelled and my English bias, I'd say ee-DURN, and it sounds lovely both ways!
Several Basque dialects also have no obvious stress on syllables so Edurne can also be pronounced simple "eh-door-neh" or "eh-dur-neh".