As King Christian X of Denmark was also the King of Iceland at the time of her birth , the Princess was given an Icelandic name , Ã Ã rhildur ( spelled with the Icelandic thorn character , simplified as `` th '' ) . Since King Christian X was also the King of Iceland at the time , as a tribute to the people of Iceland , the Princess was given an Icelandic name , Ã Ã rhildur ( spelled with the Icelandic thorn character , simplified as `` th '' ) .