Even within Wikipedia, the wording "2000s decade" is much clearer than "2000s".
In keeping with naming decades (cf. 1990s "the Nineties", 1980s "the Eighties", etc.), the decade of the 2000s lacks an accepted name. A widely accepted term most likely won't come about until the decade has ended, but a few possibilities are:
"the 0-0s", usually pronounced as "the oh-ohs". This pronunciation sounds like "uh oh", an expression of dismay; this similarity is no doubt intentional.
"the 2Ks", a term that is rooted in the slang of the times. K is shorthand for the Latin prefix kilo meaning 1000; hence, 2K means 2000. In popular culture, the years of the decade are already being named according to this slang. For example, the year 2003 is referred to as 2K3. The "2K" term probably has its popular origins in the heavily-hyped Y2K bug that began the decade.
"the Aughts" (or "Oughts"), keeping with the practice of the nineteenth century.
"the Nillies", derived from the term "nil", meaning nothing or zero.
"the Noughties", referring to the nought, or zero, as the decade indicator; the word-play on "naughty" is intentional.
The United Nations General Assembly declared the (mostly overlapping) decade of 2001-2010 as the "International Decade for a Culture of Peace and Non-Violence for the Children of the World".