You cannot get a domain name for free. When you type
www.anyname.com into your browser the browser looks up
the ip address for the domain name this will only succeed
if you have an official domain registered with one of the
official domain registries. If you have done this then
there are still problems.
1. If you connect to the internet through a DSL modem or
router then you need to connect the IP address of the
router to your domain name. Unfortunately the IP address
assigned by you ISP may change from time to time unless
you arrange with them to have a static address provided.