Server public hostname

So, I've got this great SSH server set up on my computer since quite a long time. The thing is, I have to memorize my public IP to access it. Tired of doing this, as I can't always guarantee my IP stays the same, I decided to lookup info about hostnames and stuff. My ISP provides me with a hostname such as MY.CURRENT.PUBLIC.IP.dyn.user whatever which solves absolutely nothing.

Even if I could change my connection settings to a static WAN address, I really don't want to, I want to have a hostname I can publicly access and most important, that points to my public IP, and that I somehow would be able to update where it points, in case my IP changes.

How can I accomplish this? Or where can I find information on how to do it?

Thanks for your attention.
 
Thanks a lot for your suggestions! I managed to get a free subdomain pointing to my IP, it was exactly what I hoped for :D I'm marking this as solved.

You guys rock.
 
As a backup, in case something goes wrong, I have my server check its own public IP every 5 min. and compare to current IP stored in file. If it changes, it emails me new IP via something like ssmtp.
Server is always on so in fact IP rarely changes. Last time it changed was about two months ago, due to power outage, so by that time I just learn it.
 
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