Hi,sorry Mr.Luke I didn't heard about the website with free domain name registration.
So I would suggest website like XnYnZ.com here you can make a website and register your domain name at low cost.They are providing free web hosting with website builder.If you register 5 or more domains you can also FREE Private Registration and many free features.They are supporting with good customer service and support at 24/7.I registered my domain name here.