In order to upgrade with minimal downtime, I ordered a new server before canceling the old one.
But the form wouldn't allow me to assign my domain as the hostname of the new server when I signed up for it because I was already using it for my old one.
So, I was advised to name my new server "srv1.mydomain.com" and after I cancel the old one, submit a trouble ticket to get it changed to "www.mydomain.com".
Well, when I made the changeover to the new server, I went into DNS Configuration and changed the pointer for my domain to the new IP address, and that seems to be doing the trick by itself.
Is there any reason that I would even need to submit that trouble ticket and have the server's hostname changed?