Ordinarily, I try to avoid explicitly contradicting other experts on Clarity.fm. However, some of the comments above are preposterously incorrect. Tom Williams and David Melamed are probably very knowledgeable in their chosen fields. However, based on their remarks here, it's quite clear that they're comparatively inexperienced with domains.

"The importance of domains names has diminished significantly and will likely continue to do so." That's a bold prediction, but I see no reason for believing it. Has social media obliterated the importance of domains? OK. Then why did the founder of Facebook pay $75,000 for the domain name Internet.org last August? Sales of that size happen almost weekly. Or has Google condemned domains to worthlessness? OK. Then why is Google itself now competing for the privilege of running a fleet of new domain extensions such as .WEB?

And the other problematic statement: " ... considering the cost of buying a domain name is less than $10 a year ... " Which domain is that? Here is a list of last week's reported sales:

http://dnjournal.com/domainsales.htm

To those 2 experts I'm disagreeing with, it's nothing personal. However, the statements above are grossly mistaken; and it's important to point that out.

In answer to the original question: Yes, there are a few ways to use paid advertising to test a domain. A/B testing in this area is actually an underutilized but important ingredient in SEM. You should test the domains using whichever PPC channel you're planning to advertise in -- whether that's AdWords or something else.

While I would advise such an approach for extending your SEM dollar, I probably wouldn't advocate paid advertising as a test to choose a domain in the first place. Unless the intended domain were a 6 or 7-figure purchase, it would simply be too expensive to run a test like this long enough to gather statistically significant data.