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',

    @srvproduct=N'MSSQL',

    @provider=N'SQLNCLI',

    @provstr=N'PROVIDER=SQLOLEDB;SERVER=GX620'

 

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

    @useself=N'False',@locallogin=NULL,@rmtuser=N'sa',@rmtpassword='P@ssword!'