Hi Peregrine,
As I understand, you want to add a CNAME which gets awverify.www.mydomain.com points to awverify.mydomain.azurewebsites.net to your domain registrar, but it doesn’t allow you to add the record value like awverify.www, you get an error. Please correct me on time if I misunderstand the issue.
If so, about the CNAME record value limitation, please consult your domain registrar for help.
In additional, about active the website hosts by Windows Azure, as Windows Azure is a different product from Office 365, in order to troubleshooting the issue effectively, I suggest you go to Windows Azure Forum for help, the engineers on Windows Azure Forum are more professional than us on Windows Azure product. You may find the Windows Azure Forum below:
http://www.windowsazure.com/en-us/support/forums/
Thanks for your understanding.
Thanks,
Eric Sun