I think the variations have more to do with lack of formal education rather than intentional changes.
My name is McKenzie, and I was told that all "Mac"s coming through Ellis Island had the "a" dropped from Mac in order to save on ink by the Immigration officials having to write each person's name around a dozen times.
Which sounds good until you know that my ancestors emigrated to America in the 1600s. I have traced by lineage and am pretty sure that MacKenzie was changed to McKenzie as early as the 1700s.
There does not seem to be any rhyme or reason to the capitalization.
Personally, when I sign my name I make the K the largest letter.