I saw your support ticket for this and I will share in here for the community what the Wowza engineers had to say:
"You would not be able to mask the wowza domain in Cloud. However if you have your own Engine instance, you could point a domain via DNS to the Engine instance, or use the IP address for the instance.’
That is correct, not possible in Cloud, but you can achieve this in Streaming Engine.
The other option would be to use Wowza Engine were you could map your own domain to this instance or be able to provide a static IP address for connection. I would recommend testing with the free Engine trial to see if you want to manage your own instances vs using Wowza Cloud.
Please see this post for reference on mapping to a domain name in the DNS:
While Cloud can be quite convenient as it handles most of the streaming process for you, sometimes customers require Streaming Engine where they have full control over settings and configurations. I’m not sure if this would be a better option for you than Cloud, but if you find in testing with the free Engine trial that it is but you have a Cloud account already, just email firstname.lastname@example.org to discuss your options and explain why.