You can clone a service directly on clicking the clone icon in the service view of a host.
You can also clone a service to other Hosts (with the clone icon in the Advanced box also in the service view)
Here you can choose which Service to clone from its host.
You you can also choose an new name for the service. If a service name already exists on a host, it will automatic add "_clone" to the name.
When the name field is empty it will take the name from the service which will be cloned
Then choose the hosts you want to clone to.