If select SQL linked server in the GUI you can't specify a different name for the SQL Server.  You can only use the SQL host name as the Link Server name.
Here is an example of creating a Linked Server via script to specify link server name myGX620 for the SQL Server host name GX620.

/****** Object:  LinkedServer [myGX620]    Script Date: 04/07/2009 22:49:10 ******/

EXEC master.dbo.sp_addlinkedserver

    @server = N'myGX620',





EXEC master.dbo.sp_addlinkedsrvlogin @rmtsrvname=N'myGX620',