A chord containing a 6, 7 and 9 - what would you call it?

[lfm]

The function in the context of the overall chord progression is the real interesting thing to find out.

The interesting thing about "jazz" chordings are that you basically run 6 out of 7 notes in a scale in just about every chord.

It's the "missing note" that tells the "context". It's a soup of notes, kind of.

I often heard Matt Johnson mention "it just works".

When you hear a clean major or minor chord in "jazz" then it really pops out.

But more into pop, rock and blues and melodies, really. 7ths and 9ths is my limit.

[jancivil]

Another take (probably very unusual):

You're playing two simple chords at the same time:
Am/C in the left hand
G/D in the right hand

The musical terminology for that is polychord:

It's not the only term there is for that, though.
Am in the LH, G in the RH amounts to an Am7 (9) (11).
A jazz chart is liable to just state Am11. In the cases where it isn't "the full 11th chord" according to that 'theory' I would use parantheses (or "add 11", even "add 4") if I had to be so clear.
C in the LH, D on the RH amounts to a C (9) (#11) (add 6) or (13). If we're dealing strictly in tertial construction, extensions of one chord might be less mentation than two chord names.

The original question posits a 7-note chord so you could call it the scale name for that matter.

[FranklyFlawless]

Yes, there is still plenty of ambiguity in music theory, so I work with what terminology I know from my perspective.

[jancivil]

Sometimes two simple chord names will be the clearer way to proceed, no question.

Sometimes resolving a slash chord into a chord name is just a waste of time, although my brain wants to do it anyway. G/C, any triad with (an otherwise no-exist) '4' in the bass needs quite some 'splainin' for example (w. extraneous language eg., "no 3rd").