Lisa's right, you're only going to get available domain names (assuming you set up for a domain) unless you ask otherwise. If you wish to expand into finding available domain names, being open to other extensions (.net, .io, .ly, etc) and setting it up for those will increase your chance of having good submissions, or as Lisa suggested you could be open to buying domain names to a certain price point (which means if namexyz.com is taken and you have put that you are open to buying domains to $xyxy price, creatives can submit names (that they do not own, and are parked by someone else) and tell you the price of such as long as it is at or below your price -- NOTE: be prepared that parked names can be hundreds or thousands of dollars but for short names or really good .com and some other extensions, this can sometimes be a good option to a great name) and then tell you the price and you can go from there and choose winner for award and then buy domain.
Otherwise, names submitted will be available and untaken (unless creative owns, as Lisa explained) and all you'll have to do is conduct contest, choose winner, and then choose a place to buy the domain (Note: there are many host domain places that you can buy open and available domain names, and each one charges different amounts to buy as well as any additional services the host offers. It's not going to be thousands but it will cost to buy the domain and services of your choice, places like godaddy and a few others can be anywhere from a few dollars to more, depending).
Edit: ... and just saw how old this was, opps