After installing WordPress on Azure using this “how to” : https://azure.microsoft.com/it-it/documentation/articles/app-service-web-create-web-app-from-marketplace/
You will have a website with an address like this: http://examplewp.azurewebsites.net
Now you have to set the CNAME on the provider’s DNS of your hosting because you want your wordpress site points to http://www.mydomain.com. You can use this “how to” : https://azure.microsoft.com/en-us/documentation/articles/web-sites-custom-domain-name/
Now go into your wordpress site, in the general configuration.
You have to change WordPress address (URL) and Site address (URL). from http://examplewp.azurewebsites.net to http://www.mydomain.com