There is no easy way to map your dynamic IP to your domain name. When you buy domain name, you will be asked to choose nameservers. Those are the ones keeping track of your name to your IP address. There you will set up which IP address will represent your domain name.
A lot of people use other services such as dyndns.org to keep track of IP address changes. But then again, the domain name becomes user-name.dyndns.org .