Fiona is, in fact, an artificial Gaelic name, made up by the Scottish poet James Mcpherson (1736-1796) in his very popular "Fragments of Ancient Poetry". He pretended that he had found medieval texts containing the orally transmitted poems of a Gaelic bard "Ossian" – in fact, he had invented the texts himself. One of the heroines is Fiona. Mcpherson/Ossian had invented the name (it did not exist before) by latinizing (-putting an -a- at the end) the name of the Irish hero Fionn. Mcpherson not only instigated a Europe wide "bard movement" where people from England to Germany, Switzerland and France got themselves a "Gaelic" name and started to invent "Gaelic chants" the way "Ossian" did (it was a real craze), he also popularized the name Fiona. Johann Wolfgang von Goethe quotes "Ossian" in his 1774 Sturm und Drang drama Werther, and both Napoleon and Mme de Stael read "Ossian". And very soon after, people started to name their daughters Fiona, not just in Scotland, but also in Germany and France. Historians call this an "invented tradition".
The name means "white, fair". It's Fionn in Gaelic, Fiona is the latinised form. I am a bearer of that name myself, and as I live in Germany (although I'm English with Welsh, Scottish and Irish ancestry) people often don't know how to pronounce it.