The next thing you need to do is try to find the shortest and the simplest possible domain. Remember, the shorter, the better. Shorter domains are easy to write, easy to spell, and easy to remember. The domain providers can offer you a subdomain of one or maybe two letters, so if you add the domain name to the subdomain, you may come up with a really cool domain name.
Usually, the domain name providers offer additional free services with the domains, for instance, free hosted DNS, free email, and etc. Try to find a provider that will give you as many services as possible.
The last thing you need to do is check the terms and conditions. Even though the provider will give you a free domain, there may be some catch in the deal. So make sure there are no strings attached and there are no additional fees you should pay in the future.
There are a few good free website name service providers out there, so if you want to build a stable business, spend time researching the domain you want to use and pick the right provider to register domain name free of charge!