In the first decade of the last century, I think people referred to it as the "aughts." They also said "back in aught-nine..." I think we don't know what to call this decade because "aught" is a word nobody seems to know or use anymore. It ought to be revived.
U: Your predictions are entirely in sync with those of Allan Metcalf, author of "Predicting New Words". he writes:
"But just wait till we approach the year 2020! Headline writers, prognosticators and pundits will welcome the twenties with open arms. Gentlemen and ladies, start your books now, with your title 'The Twenties: Decade of ...' "
I remember back in '99 there was a "Name the Decade" web site that took votes to decide what the "official" name would be. This word (Naughties) won. But now nobody's ever heard of the site, and apparently it didn't have much authority over such matters anyway. ;-)
Actually, I find it interesting that before 2000, decade names were common in regular speech: I always heard people talking about "the '90s" or whatever decade it was at the time. Now, not so much. Because nobody can figure out what to call this decade, nobody does. Occasionally you'll hear "the new millennium" or "the 21st century" used in that place, or in some cases even "the post-9/11 world." But it's almost as if society collectively just stopped naming decades.
I suspect we'll start again in the '20s, but that'll just seem wrong to me after experiencing much higher numbers. It's like a step backwards to me, it doesn't seem like progress or "the future." Maybe that's because it conjures up thoughts of the Roaring Twenties and I'll always associate it with talkies and flappers.