The idea that there are correct and incorrect ways to spell words is a fairly modern notion, dating back to only the first half of the 19th Century, less than 200 years ago, when dictionaries were first introduced. Before then everyone spelled words as they sounded to them. So Mac, Mc, M', and other variations are all equally correct or equally incorrect, as is whether the patronymic prefix is separated from the rest of the name.

I have a copy of a deed from the 1750's in which my surname was recorded in the index of deed book under one spelling, spelled a second way when the clerk copied it in the body of the deed, and shows my ancestor's signature's having been copied in a third spelling, presumably by the same clerk, the way we happen to spell it today.