Yes, you should visit websites like
http://dyndns.org, these give you a domain name and your server wil sync with this website when it changes its IP address, thus always directing to the new IP address. However, you need to also make sure that you have a real, external IP address, accessible from the internet, and not just an IP address that is internal to your ISP. This could be dynamic, too, but unfortunately there's no way an internal IP address will be directly accessible from the internet (without setting up a VPN, or redirecting traffic over another server with a real IP address), since it is exclusive to the ISP. In such cases, the ISP acts as a transparent proxy.
Websites like
http://www.whatismyip.com can give you your IP address and identify it. If the IP address is identified as your ISP's address, you can be pretty sure that it is not your own real IP address.