Definitions of verbalisations in card games, specifically UNO and DOS
It doesn't say in the rules and since both words ("UNO" &amp; "DOS") are so short it really shouldn't be an issue...  

http://www.mattelgames.com/sites/mattel_games/files/2018-03/FRM36-0970-G2_IS_web.pdf

But, I would say that it's quite clear that as soon as someone starts to say the word, no one else is allowed to also say it - but faster.  

You could compare it to the first person to press a button or the first person to shout their name in a game show.
The first person to press the button gets to answer - Not the first person to press and also release the button...
The first person to start saying their name gets to answer - Otherwise the person with a short name would always be favoured over the one with a long name...