If you need rename linked server, you have only one way.
You must update sys.serveres table. This is possible only if you are in DAC mode (dedicated administrator connection).
WARNING: From now on (until ages) always after the sql server startup you will see the following warning.
WARNING: System table ID 43 has been updated directly in database ID 1 and cache coherence may not have been maintained. SQL Server should be restarted.
select * from sys.servers