In some situations when you are creating a linked server you will want a name for the object that is different from the machine name.
This is mostly the case when you are connecting to a machine outside the domain and you can only provide an IP address for the server name. Obviously, when having more than a few of this type of linked server it will be difficult to associate them with a location or scope and having a friendly name would be useful.
Unfortunately, the UI is limited regarding this type of action, but the T-SQL comes to save the day (as always).
Here is the solution for having a different display name for a linked server:
@server = N'MyServerName'