Hi there, as far as i understood from your post, you are looking for a service called DDNS, you might want to do some search on that by googling something like DDNS services and understand what that services does for you, also, i would like to suggest you to try this service provide : noip.com. Note that you can achieve the same result with DDNS record that is supplied by SE server, but it's not worth going through installing the SE server for only that purpose, let me know if you would like to get more technical details about the setup that is associate with DDNS service.
Good luck (: