With Azure SQL Database, you can choose the server name:
Once you select the option to create a new server, you see similar options to those you saw in the Azure Management Portal. However, this time you see a server name.
Alas, you can again name your own database servers! As you can see above in the Azure Preview Portal, the server has been created with the provided name. Then if we switch over to the Azure Management Portal, we will see the same.
Choose your names wisely.