"Are your names Willem and Roos?"
Translation:Zijn jullie namen Willem en Roos?
Uw is just the formal way of saying "your". Also, "zijn jouw" is singular (referring to one person), where "zijn jullie" is plural (referring to more than 1 person) so basically you would use "zijn jullie" or "zijn uw" for the above sentence :) If it was a listening exercise that specifically said "zijn uw" though, you would have to dictate it that way.
What you are saying then is "Are your names to want / want and Rose?". Maybe here it is a fairly innocent mistake, but a single letter can make a lot of difference.
To stick to English: Pace and Lace are only one letter different and very different, same with Now and Mow, Rub/Tub/, Blow/Glow etc.