Invented name, possibly intended as a variant of June. This name was brought to limited public attention by Basque animation film 'Gartxot' (2011). In the film, Xune is a girl who befriends the main character Gartxot and wants to become a minstrel like him.
From Asturian xunetu meaning "July". This name was popularized by musician Xulio Andrés 'Xune' Elipe, who, after asturianizing his name from Julio to Xulio, received as a nickname the translation of julio ("July") into Asturian (xunetu).