I'm not sure about what it was referred to then, but now I've heard it referred to as the aughts (or the nineteen-aughts). The confusion is that we're now past that time in the 2000s, so that is also referred to as the aughts.

Through most of my classes it's simply been referred to as the early-1900s or turn of the century, although I feel like those will be outdated at some point simply due to time.