A strange phenomenon that I came across was based on the following error that occured directly after a server rename that was performed exactly as described in this article:

Server 'test-sql2' is not configured for DATA ACCESS

In order to rectify the problem I ran the following statement:

exec sp_serveroption 'test-sql2', 'data access', true;

And that was the problem resolved.

My only advice to those planning to rename a SQL Server is to test the renaming process on a disposable server so that there is nothing in your environment that could be adversely affected. The resolution to this problem took an hour of zero productivity on the server to resolve!