You cannot create a local SQL Server as a linked server

If you try to create a linked server to itself you will get the next error:

There is  a trick to do it, it is called loop back linked server.

In the Linked server textbox instead of providing the name of the SQL Server instance, type "." (only dot). This will indicate the linked server is a loopback linked server.

On the Security tab, choose "Be made using the login's current security context" select option.

Click the OK button to finish adding linked server to SQL Server which points to itself.

In Object Explorer window, you will see the new loopback SQL Server linked server with "." as the name.