OSMC uses systemd not upstart like Raspbmc did.
So the whole way that services are loaded and managed has changed. There is some backward compatibility between systemd and sysvinit services but it is not 100%.
I’m not familiar with ddclient so can’t offer any specific advise to fix it but I can suggest a few things:
The proper systemd commands to start, stop, enable and disable services are:
sudo systemctl start name
sudo systemctl stop name
sudo systemctl enable name
sudo systemctl disable name
Where name is ddclient in your example. To check the status of a running service to see if it is running and any recent output you can use:
sudo systemctl status name
Running a script directly as /etc/init.d/ddclient start is unlikely to work properly.
You may want to read some of the documentation for systemd services to familiarise yourself with it, or contact the author to see if their package can be updated to be properly compatible with systemd if it is not.
Finally it could be that the service needs to wait for network before running, in which case you can run the following command:
sudo systemctl enable connman-wait-for-network
Which will configure OSMC to wait for the network to be up before launching services that need network access. For this to work you will need to make sure you update as this functionality was not added until after Alpha 4.