To replace a database name with a query in MS SQL Server, one of the 2 ways below should be followed.

EXEC sp_renamedb {Old Database Name}, {New Database Name} or ALTER DATABASE {Old Database Name} MODIFY NAME = {New Database Name}

Examples of usage patterns are given below..

EXEC sp_renamedb 'oldDBName', 'newDBName' or ALTER DATABASE oldDBName MODIFY NAME = newDBName

Note : When the code is run, you will see that the database name has not changed in the left panel (Object Explorer). To do this, right click on the Databases folder and perform Refresh.