From your question it is a little bit unclear which database you're using -
If you're using 'Windows Azure SQL Database' (i.e. the PaaS version), than you need to ensure that your server's firewall, through the Windows Azure Management Portal, is configured to allow Windows Azure Services and then, of course, you need to use the fully qualified name of the server when trying to connect (i.e. ABCD.database.windows.net
)
If you have deployed SQL Server as a VM on IaaS you have two options - either define an endpoint for the VM to open port 1433 (or any other port mapped to 1433 for that matter) to the outside world and then use the cloud service's DNS entry to connect to the database or define a virtual network onto which you will deploy both your database VM and your application VM. if you do the latter you will be able to refer to the database using it's private IP.
this might be somewhat useful