The name of the default instance is "default," but that doesn't get displayed in the Console.

When you create a connection in the Console you can supply a name for the connection, which gets displayed in the tree instead of the address/instance name. For example, you could create a connection to the default instance and call it "Instance 1," and that's what would show up in the Console. But each user would have to do this when creating the connection in the Console.

It's probably possible to rename or delete the default instance but that's not something we've thought through or tested, so we can't support it and you shouldn't do it :)

Each instance runs as a separate Windows service, so you can just to stop the service for the Default instance and disable the service so it doesn't get started up. The instances all share the same installed software components, so the disable instance won't be wasting any resources, other than that you'll see the disabled service in the services list.