Although my suggestion for “Naughties” for the years 2000-2009 never caught on during the actual decade (I still have hopes for retroactive adoption), there is still time to give our current decade, 2010-2019, a name.
So, here’s my suggestion: The Teenies.
2010 would just be known as Teeny. 2011 would be Teeny-one, 2012 would be Teeny-two. 2019 would be Teeny-nine.
Again, good people of Earth, go forth and proselytize. We are just starting out in the Teenies, but if we try hard we can make them the best Teenies of all time.