I can't seem to be able to deploy a site to a windows server 2012 r2 running IIS and Web Deploy in Azure VM. I have verified that the port is open, the credentials are correct and the site name as well. I tried using http: and https: also tried using msdeploy.axd end point and the MSDEPLOYAGENTSERVICE one nothing. Check is the services are running and if I can connect to the machine which at can on port 80 to the default site. Tried connecting from multiple connections I get the same result...
Could not connect to the remote computer ("<computer name>.cloudapp.net"). On the remote computer make sure that Web Deploy is installed and that the required process ("Web Deployment Agent Service") is started. Learn more at: http://go.microsoft.com/fwlink/?LinkId=221672#ERROR_DESTINATION_NOT_REACHABLE. Unable to connect to the remote server.
You don't mention if you have an endpoint configured for your Azure VM. If not, make sure you create an endpoint with a private port of 8172.
EDIT: Here is a troubleshooting guide for web deploy that includes the error message you've encountered. Additionally, from my own experience I have managed to mistype the site name and not install .NET and seeing similar errors.