These vocal syllables for note names are collectively called the solfeggio and are said to have been invented by the Benedictine monk Guido d’Arrezzo almost a thousand years ago.
The names do/ut, re, mi, etc. didn’t refer to specific notes but rather the positions of notes in whatever scale you were using at the moment. Do of course was the first step, re the second, and so on.
Just when you thought it couldn’t get more confusing, the solfeggio also has names for the half-steps between the notes of the scale, when you started working with minor keys, and those names depended on whether you were going up or down the scale. Grab a seat in front of the piano and sing along! Starting from middle C, going up, hitting every key along the way.
do, di, re, ri, mi, fa, fi, so, si, la, li, ti, do
Doing the same thing, going down from C above middle C:
do, ti, te, la, le, so, se, fa, mi, me, re, ra, do
Thanks to http://www.encyclopedia.com and Contemporary Music Theory, Level Two by Mark Harrison for the preceding information.