Hello The answer to your question is indetermined. People have been debating this since 2001, whether or not to call it twenty-oh-one or 2 thousand one. Even though 2010 is coming soon, it is still somewhat unclear whether the English speaking world will tend to call it twenty ten or two thousand ten.
I have heard many references to later future dates such as 2036, and 2029, and even 2013 or 2014 where the twenty thirty six, twenty twenty nine, twenty thirteen etc. model has been used by the media and by the general public. So it is likely that after 2020 people will switch to the twenty model.
But between 2010 and 2019 I think you will see a mix.
I personally think we should start saying it at 2010, as twenty-ten, but there are many different opinons. Others suggest switching at other dates. On the other hand, it seems clear that a switch will take place, just not sure exactly when.