Grant Fritchey shows us how to restore a database hosted in Azure SQL Database:
The first, and most important thing to notice here is that it’s supplying me with a new name. I can change that to anything I want as long as it’s not the name of a database already in existence on my Azure SQL Database Server. You read that correctly, you can restore a database to Azure SQL Database, but there is no WITH REPLACE option. The restore creates a new database. This is important. In a recovery scenario, you need to be sure that you’re prepared to deal with this fact. How could you replace the existing database? Immediately run a pair of ALTER DATABASE commands to change the name of the existing database to something else and then change the name of your newly created database to the old name. That’s your choice.
There are a couple of gotchas, so if you are administering Azure SQL Database instances, be aware of these.