Here is a short list of popular domain registrars. You can find more by doing a simple web search, and you should also do a final search on your chosen registrar to make sure they are somewhat reputable.
Remember that once you register a name, you need to use your registrar's online portal to configure a nameserver record that points to your static IP address. This is a very common task that is easily done through the registrar's control panel. It doesn't matter what host name you use for your nameserver, something like
will work fine, and it won't be visible to regular visitors of your site anyway.
Some registrars also have a free DDNS service that could be useful if you don't have a static-IP internet connection. Super Simple Server has a built-in DDNS update client. More information about DDNS is here
If you have any suggestions for this list, please visit the forum