I call that decade the "aughts". The problem with 2000s is it could refer to the 2000-2009 decade or the entire century 2000 onward. I suppose the 21st century is a better way to refer to the century, but even that has a double meaning as it's often used to refer to anything modern. However, the early 2000s are now longer really modern. There is a lot of stuff that was big at the turn of the century that is obsolete now and an entire generation of people have only lived in this century. I now feel like an old geezer talking about growing up in the 90s.
Yeah, I just say the 2000's. - I realize that doesn't accomplish much, since the 2010's and 2020's are also technically the 2000's...but, I would just clarify by saying 20-10's or 20-20's. Honestly, I would probably just say "the early 2000's" if I was having a conversation with someone...and if I knew an exact date, then I would just say 2002 or 2006 or something.
huh, i had no idea there were different ways of pronouncing it! i’ve only ever heard people call them the 2000’s (two-thousands), and i pronounce it that way as well.