I believe that the “Markdown Mark” (M↓) is liable to create confusion here as CommonMark is a variant (albeit a completely backwards compatible) of the original format. I believe having a completely new logo would do well to distinguish from the original format and show that it is an improvement.
Of note, as an outsider to this entire process, when I first went to the CM website and I saw “That’s what we call CommonMark. M↓”, I actually read it as “That is why we call it CommonMark Markdown”. Since the word “down” isn’t in the “CommonMark” name I’m not sure I agree it should be in the logo.
I think something like “CM➡” (C M right arrow, or “C M Forward”) would be great.