We don't need to refer to the third millennium as a whole right now, being in the first part of it. And by the time people need to refer to the 2000s, they wil

We don't need to refer to the third millennium as a whole right now, being in the first part of it. And by the time people need to refer to the 2000s, they will no longer have a reason to reference the 2000s. You can also refer to, in speech, the twenty-hundreds, without ambiguity; I suppose, if you want it more compact in text, you could always write the 20-00s.