Sounds like you need a DynamicDNS service like those provided by no-ip.com or dyndns.com.
When using a DynamicDNS service, a client installed on the server identifies the public ip address much as b0uncer described and reports it to the DynamicDNS provider. The ip address is then associated with a unique name of your choice like myjob.is-very-bad.org
and made available through their dns servers as a fully-qualified domain name (FQDN
To connect to your server, you would supply its FQDN as myjob.is-very-bad.org
and the magic of the internet will do the rest.
The simple DynamicDNS no-ip.com and dyndns.com services are free, but there are some nice low-cost options that you may want in the future. I use dyndns.com and have about 15 systems being tracked this way.