You would have to actually buy a domain name, for example through godaddy.com and then map that to your home IP address.
Honestly I would just write down your IP address in your phone (to remember it) and use that to connect to your home PC via SSH. On a side note, make sure you have a very long password that contains letter, numbers, and special characters. Also, try running SSH on some port other than 22. Those two precautions will enhance your security a great deal.