After stumbling onto this site, it may be worth a mention that the clan MacWilliam (Mac meaning "son of") was a highland clan existing from early 11th century to the latter part of the 12th century until warring and conflict from neighbouring clans severed their lineage and forced them apart. Once this "extinction" of sorts occurred, some members were assimilated into clan Mackay, Gunn, and MacFarlane as we know today. Although MacWilliam isn't what we're debating today it should be noted "Mac" meaning "son of" is consistent with "son of William" hence Williamson, as surnames have an evolution of their own.
http://www.electricscotland.com/webclans/m/macwilliam2.html