No matter if you use a DHCP connection (which means you have a different IP address for each connection – every 56k and ISDN line, and some DSL and Cable lines) or a static IP one, if you have a server installed on your machine, you may take advantage by "changing" your IP with a named address (for example, "yournick.hn.org" instead of "18.104.22.168"); for instance, the users of your server would easily remember your address.
This can be done for free, using both a service which mantains a DNS (Domain Name Server – a server which is capable of telling you the IP corresponding to an alias, like "yournick.hn.org", that would correspond to "22.214.171.124" as in the example above), and a small program which checks your IP every "n" minutes, and if it changed since the last time, sends the updated information to the service itself. So, very briefly, someone who knows you have an FTP server responding, for example, at the address ilikecandies.hn.org, port 21, would have his FTP client asking to the DNS of the service to tell him your true IP, and then would directly connect to that IP… still the only information he must remember is "ilikecandies.hn.org", and not your true IP, which is much more difficult to keep in memory).
To the practice now: there are more than one way to achieve this, and they depend from the small program you use to send out your IP. Every free service suggests free utilities to update the IP automatically, and since I wrote this guide years ago, the only service still operating is DynDNS.org.
DynDNS allows you to choose aliases different from the principal domain (which means, you can get "yournick.dyndns.org", but also "yournick.mine.nu", "yournick.homeip.net", and several others).