Changing Properties of a Linked Server in SQL Server
In SQL Server management Studio click right on the linked server, choose "Script Linked Server as' then choose 'DROP and CREATE to' and then "New Query Editor Window'. You can now adjust any settings that you want to adjust in the script and then run it. The existing linked server will be dropped and a new one created.
Here's the command.
EXEC master.dbo.sp_serveroption @server=N'<SERVERNAME>', @optname=N'name', @optvalue=N'<NEWNAME>'
Replace 'SERVERNAME' with the current name of the linked server. Replace 'NEWNAME' with the new name you want to give the linked server.
The only option you have is to use sp_setnetname. You can use it to change the data_source of the linked server (destination), e.g.:
DECLARE @name sysname = 'SRVRNAME', @datasource sysname = 'srvr.name.com';
EXECUTE sp_setnetname @server = @name, @netname = @datasource;
I was able to change the name of a linked server using sp_serveroption with the @optname=N'name'. This option does not appear to be in the BOL documentation on sp_serveroption.