This post will cover how to move an Azure SQL database from one Azure SQL Server to another.
I have created two Azure SQL Servers in different regions, and both servers have a single database that we are going to use to perform this test.

The databases will have a database user login associated with them. All current database logins are copied over to the new database once the copy activity is done. The SQL Server admin credentials are, however, not copied over.

You should note that the security principal you use to copy over the database will become the new owner of the database (Administrator at the new Azure SQL Server).

We are going to copy test-db01 to a new Azure SQL Server over at test-sqlserver02. The database maintains a transactionally consistent copy of the database from the time you initiated the copy activity. Any changes after that copy activity are not copied over, so it's good to inform any users before this activity.

Select the database that you want to copy and click on the copy button.

The copy button should pop up on the screen shown above, and then you should change the database name with destination Azure SQL server as shown above when done, select review and create.

That's we should now be able to access our database on the new Azure SQL Server.