We would like to be able to use a Custom Domain name url for Microsoft Managed and Cloud Hosted deployments. Most likely the easiest way to do this would be to have a domain (or sub-domain) hosted in Azure that all the Dynamics deployments would use.

For example:

mycompany.com (hosted by the company or someplace else)
dynamics.mycompany.com (hosted by azure)

Each deployment would create a new sub-domain in the azure hosted domain/sub-domain.

Development: dev.dynamics.mycompany.com
Test: test.dynamics.mycompany.com
Production: prod.dynamics.mycompany.com