Let's imagine the worst happens: John Gruber explicitely refuses to give up the name "Markdown", and to bless any standardization process. Which would then need another name.

Ideally the name should be clearly different than the original one, and clearly signal the underlying spec is the same, only better (of course, the actual spec better live to that expectation).

"Rockdown" sounds cool, but it doesn't work. Sure, it rocks, but it's doesn't say "you should use me, not my obsolete father".

An obvious choice is "<qualifier> Markdown". For instance, "Clean Markdown", or "Standard Markdown". We may think that's cheating, but we already talk about "<website> flavoured Markdown". There will soon be another one, that explicitly pretends to be the flavour. Better let the name reflect that. As for the actual Markdown, I guess people will start calling it "Original Markdown".

Now there's little chance, but maybe, maybe John Gruber will still shout that his original version is the standard no matter what. If monsters like Stack-overflow, Reddit, and GitHub make a good "std Markdown" anyway, no one will believe him.

Anyway, enough with the name. Let's just write that BNF. A reference implementation in something like MetaII or OMeta will then be a piece of cake. If I ever do that on my own, I'll call it "Strict Markdown". Because I don't like when obvious errors in my Markdown code produce unintended output instead of an error message (major culprits are links and emphases).