As an English name, Una is considered both a borrowing of Irish Úna and Scottish Ùna and a name in its own right derived from Latin una "(female) one". In the English-speaking world, the name has been in use since the 17th century and features in Spenser's The Faerie Queene.
Variant of Hunna. Saint Una or Hunna (died ca. 679) is a French saint who devoted herself to serving the poor women of Strasbourg, France. Because she undertook to do the washing for her needy neighbors, she was nicknamed by her contemporaries "The Holy Washerwoman".
Either inspired by the name of the river Una (bordering Croatia and Bosnia-Herzegovina), whose meaning is uncertain but could be from Latin una "(female) one", or directly from Latin. It's a modern name, used since the 20th century.