1. Find some available domain names that are, at the very least, easy to pronounce and spell. Easier said than done of course, but I still think it's possible to find some good stuff. For example, this website - http://www.5letter.com/domain-names/ - allows you to search through all available domain names that are exactly 5 letters long. There are some surprises there.
2. Register as many domain names as budget allows. If it sounds good and its available, grab it.
3. Throw together a website with a bit of info about your product and a box for people to enter their email address to find out when you're launching. I'm sure you have seen these kinds of sites before. The whole point of doing this is to make sure people have something to look at when they click your ads, and you might get to collect a few email addresses to notify when you DO actually launch.
4. Go to Google adwords and set up an account (http://adwords.google.com). Create an ad that explains something about your product. Clone this ad for each of your domain names - ensuring that the ad title contains ONLY the text in each of names to test. For example, if your domain name is XYZ.com then put XYZ in the title. The point of this is that all your ads will be identical EXCEPT for the title, which contains a potential product name.
Make sure all the ads point to the website created at step 3. Choose keywords that people in your target market will be most likely to search. Make sure your budget is high enough to ensure a reasonable statistical sample for each ad. You need enough, in my opinion, to collect at least 100 clicks per ad. Google can handle all of the ad rotation for you, though there's no guarantee that impressions will be equal for all ads.
5. (I'm currently at this step). Launch all of the ads. Wait for a couple of weeks or for however it long it takes to get a statistically reasonable number of clicks and impressions. Once you're happy with the numbers, look at the click/impression ratio for each ad. Basically, the ad with the highest ratio of clicks to impressions "wins", and the name in the ad title is your product name. If there's no clear cut winner, the idea is to cut all the losers and re-run the top 2 (or 3 or whatever it is) until a clear winner is found.
A couple of things about this method:
a. The method costs a bit and can take up a bit of time. I've spent about $300 so far, and some of the ads still haven't got enough impressions yet after two weeks.
b. You obviously don't need to actually register all of the domain names, but I still think it's a good idea just in case you miss out on a good one. You don't need to create the website either, but I think it's a good idea if you're serious.
c. I'd imagine this process might work well for product names in general.
d. There's a chance you'll get to a sort of local maxima with your choice of names. No idea how to resolve this, short of coming up with as many different ideas as possible.
e. Probably won't work too well for products aimed at hardcore geeks, as they don't tend to click ads or block them altogether.