There are a few settings that may need to be changed.
In the CompleteFTP manager, there are Advanced Settings for each protocol. If the customers has explicitly set IP addresses in “Listening IP addresses”, these will need to be changed to the new IP address (the default, which is listen on all interfaces, does not require changing).
If they are using FTPS or HTTPS, their SSL certificate is likely to have the hostname set in it, so the certificate will need updating.
if they are using FTPS, they may have the “External IP address” set in the Passive Transfer Settings”, and that may need to be updated if the external IP address is changed.
Firewall settings should be updated if they reference the server’s IP address.
Clients using SSH/SFTP/SCP will likely have the IP address or hostname recorded in their known_hosts file or equivalent, which allows them to check the server key against the hostname or IP address. So clients will need to update these.