If your server has ConfigServer Security and Firewall installed (CSF), then you may find it necessary to whitelist a hostname as opposed to an IP address.
CSF has a file specifically for allowing hostnames called "csf.dyndns". Fully Qualified Domain Names (FQDN) are checked at a configurable interval of seconds, to poll for a change in the IP address.
Please note:
This will require root access via SSH or console and some command line knowledge to complete.

To whitelist a hostname:
SSH to the server
Open the file "/etc/csf/csf.dyndns" in your preferred text editor and add the hostname.
Save and exit the file.
Open the file "/etc/csf/csf.conf" and set:
DYNDNS = "300" (which would check for IP updates every 5 minutes).
Note: If you want the activity of the IP also ignored, set DYNDNS_IGNORE = "1"Restart the firewall.
You can do this via the CSF interface inside of WHM or by using the command “csf -r”
That's it. The hostnames in csf.dyndns will automatically be allowed and the rules will refresh every 5 minutes.