To indicate Markdown support, we propose using the Markdown Mark by Dustin Curtis:

Vector and PNG downloads on GitHub:
https://github.com/dcurtis/markdown-mark

Dustin kindly placed this logo in the public domain, so everyone is free to use it.

Given the shift of name to remove Markdown completely, is it still important/appropriate to use the Markdown logo? I think the down arrow in a logo for something without "down" in the name creates confusion.

CommonMark is fully Markdown compatible, so the logo indicates that compatibility.

I'd presume the same with any other implementation that supports Markdown.

Just to give you advance warning, I think that speakers of British and Australian English are going to find it hard to read or say "CommonMark" without hearing and thinking of a more familiar phrase – which was used as the name of a TV series:

Could risk abbreviations rhyming with 'duckdown', and logo derivations like this:

I still think it would have more charm and distinction as JAM – Jeff Atwood Markup – extension .jm – in tribute to the systematising rigour of John MacFarlane.

A jam jar would be a more appealing icon, and while jam.org is taken, markjam.org remains terra nullius.