From CELTIC NAMES FOR CHILDREN by Loreto Todd (Dublin: O'Brien Press, 1998): "Siobhan, Shevaun, Chevonne, Siubhan, Siun... All of these names are versions of Susan, meaning 'lily', or Joan, meaning 'God is gracious'."
From IRISH NAMES FOR CHILDREN by Patrick Woulfe (Dublin: Gill & Macmillan Ltd, 1967): "The fem. form of Joannes, or John, which became common in France in the twelfth century as Jehanne and Jeanne, and in England as Joan; brought into Ireland by the Anglo-Normans, where it has ever since been one of the most popular of women's names."
From IRISH FIRST NAMES by Ronan Coghlan (Belfast: Appletree Press, 1985): "The Irish form of Joan (which is sometimes rather sloppily rendered Siun in Irish), a name which was introduced into Ireland by the Anglo-Normans."
From A CONCISE DICTIONARY OF FIRST NAMES by Patick Hanks and Flavia Hodges (Oxford: Oxford University Press, 1992): "Irish Gaelic form of Joan... derived from the Anglo-Norman form Jehanne."
All of the above are authorized, Irish and United Kingdom sources. Would you care to give us your source of information? I checked a few Gaelic dictionaries, and so far haven't been able to find "siobhan" as being the Gaelic equivalent for the English word "white".