The Name

While the various beginnings of the McFadden family are unknown, the etymology of the name is quite clear.  It and its variants are universally considered to be anglicizations of the Gaelic (or Middle Irish) Mac Pháidín or Mac Páidín, which mean “son of little Patrick.” It should also be noted that centuries of poor literacy and general indifference towards the spelling of surnames has led to many similar names being absorbed into each other. As a result, there may be some overlap between Mac Pháidín names and those that sounded similar (Ó Peatáin, Ó Faodhagáin, etc.) or those that were also derived from Patrick.

Though it took hundreds of years for the entire populace to follow suit, hereditary surnames in Ireland and Scotland generally came into being between the 10th and 13th centuries.  Most of Ireland and Scotland shared the common language of Middle Irish at the time.  Thus, whether the Mac Pháidín family or families originated in Ireland or Scotland, their name is assumed to have become hereditary during a time when both places spoke the same language, or at least versions of it.  That explains why there may be unrelated Irish and Scottish families with the same name.

Sources:

Woulfe, Patrick. Sloinnte Gaedheal Is Gall: Irish Names and Surnames,. Dublin: M. H. Gill & Son, 1906.
http://www.scotlandspeople.gov.uk/content/help/index.aspx?560
http://www.scottishhistory.com/articles/misc/macvsmc.html
http://en.wikipedia.org/wiki/Middle_Irish