Add a nickname for your server in ~/.ssh/config, and turn off CheckHostIP for this server.
Host nickname
HostName example.dyndns.org
CheckHostIP no
Before you connect to the first time, you can copy the public key out-of-band: grab /etc/ssh/ssh_host_rsa_key.pub from the server, remove the root@hostname part at the end of the line, add example.dyndns.org at the beginning, and append the line to ~/.ssh/known_hosts. Optionally run ssh-keygen -H to hash the host name (this is only useful if you're concerned about the privacy of that entry if someone steals your hard disk or your backups, which for 99.99% of people is useless because the information is present in some other nearby location anyway).