I suspect the abbreviation M'Cheyne has to do with the difficulty of producing
M'Cheyne (with a superscripted "c") on an old fashioned typewriter/typesetting. The name itself is clearly Mc-Cheyne but even in the computer age, I can't figure out how to produce it on this site. I tried cutting and pasting it and the site autocorrected it to a quotation mark! In contrast, producing a quotation mark is easy.
That's the problem I had. I don't why the Puritan Board's software thinks it knows how to spell better than we do!