To change the logical name of the SQL Server databse one can follow the steps below to change the logical name of database data file and log file. You may want to take a backup of the database before applying the change to ensure you have a rollback.

Example:
Use test
select fileid, name, filename from sysfiles
fileid name filename
1 test C:\MSSQL\Data\test.mdf
2 test_Log C:\MSSQL\Data\test_log.LDF

— rename data file
ALTER DATABASE Monitor MODIFY FILE (NAME = test, NEWNAME = App_Data)
GO
— rename log file
ALTER DATABASE Monitor MODIFY FILE (NAME = test_Log, NEWNAME = App_Log)
GO

— verify change
select fileid, name, filename from sysfiles
fileid name filename
1 App_Data C:\MSSQL\Data\test.mdf
2 App_Log C:\MSSQL\Data\test_log.LDF