Two thousand was obvious.
Two thousand and one as well, thanks to Stanley Kubrick.
I made a determined effort somewhere around 2004 to go back to the previous century’s naming, and call the first decade “aught,” as in “twenty aught six.”

Nobody followed me in that.

Even so, I now refer to all years except 2000 and maybe 2001 as “twenty (aught/oh) <year>.” Good riddance to “two thousand seven” as a year.