@gjo on the host itself, you can look in the fog client log. You can also look at the “PC properties” and see it’s domain status. in Active Directory Users and Computers, you should see the new computer object. A note on this you might not be aware of, FOG will rename the system to whatever name you have set in the FOG Server for that host, it does this just before domain joining.
When I was doing a lot of imaging, we would set the hostname during Host Registration.