MS-SQL / Rename a computer that hosts a stand-alone instance of SQL Server

For a renamed computer that hosts a default instance of SQL Server, run the following procedures:

EXEC sp_dropserver '<old_name>';  

GO  

EXEC sp_addserver '<new_name>', local;  

GO

Restart the instance of SQL Server.

For a renamed computer that hosts a named instance of SQL Server, run the following procedures:

EXEC sp_dropserver '<old_name\instancename>';  

GO  

EXEC sp_addserver '<new_name\instancename>', local;  

GO

Restart the instance of SQL Server.

After the Renaming - Verify renaming operation

Select information from either @@SERVERNAME or sys.servers. The @@SERVERNAME function will return the new name, and the sys.servers table will show the new name. The following example shows the use of @@SERVERNAME.

SELECT @@SERVERNAME AS 'Server Name';  

https://docs.microsoft.com/en-us/sql/database-engine/install-windows/rename-a-computer-that-hosts-a-stand-alone-instance-of-sql-server?view=sql-server-ver15