How can I find a catchy name for my startup?

Make it immediately recognizable as being related to the subject of your company (unless you're a completely new service, then you could possibly get away with more obscure names). And make sure you can pronounce the domain name without having to spell it out. There's way more to consider, but I would read the following that covers it in way more detail than you could in a post here.

From Dharmesh's own blog - here's an article that covers the process of coming up with a name: How To Pick A Company Name - Tips From The Trenches

And one more that provides a lot of great insight into the criteria that the name should meet: 17 Mutable Suggestions For Naming A Startup

PickyDomains.com is a $50 service that you only pay for if you select one of the names they suggest. You can provide some guidelines (though I've heard mixed reviews on how well some of the suggesters follow these guidelines), and a bunch of people suggest relevant domain names. Cheap way to crowdsource it.

Crowdspring runs naming contests with awards starting at $200. You might get some good results there, but would most likely need to offer more than $200 to get more participation by creatives. Make sure you give feedback on all submissions in order to get more and better submissions, and I also suggest that you eliminate submissions you don't like rather than give them a low rating because by eliminating them, you immediately free up the creatives to submit more since they are limited to 10 at a time.

There is a company called Igor that specializes in naming and branding. They have a 122-page Naming Guide in PDF format freely downloadable, you don't even have to register. (The short version for the impatient ones is 20-something pages.)

Disclaimer: I am in no way affiliated with that company. Just recalled coming across it a few years ago. By the way, I have recalled it by name easily, albeit "Igor" does not look too catchy nor is immediately associated with naming and branding. Hmm...

It doesn't need to be catchy, first try and create a list of name ideas yourself, while searching on godaddy or another for availability, take a look at the suggestions/alternatives, i dont suggest taking one of these but sometimes there can be a word within those that you might not have thought about.

I got a great domain years ago while searching on godaddy this way.

I recommend reading http://onstartups.com/tabid/3339/bid/17702/17-Mutable-Suggestions-For-Naming-A-Startup.aspx and http://messymatters.com/pgnames.html to help you narrow it down, there are other things more important than catchy, i would avoid trends of adding an r onto the end of a name.

In the UK there are currently ads on tv for two separate companies with what i feel are bad choices for domains, one is called trivago which they end up spelling out near the end of the ad, a bad sign i feel.

Another is called voyageprive, easily misspelled, i actually misspelled it seconds ago while looking for the name, bit of a mouthfull too.