Changing @@SERVERNAME causes SQL Server Backups to Fail for AlwaysOn Availability Group

One of customers changed the value returned from @@SERVERNAME.  SQL Server works no problem, however an unexpected behavior appeared.  Changing the value for @@SERVERNAME, caused the backups to fail. Looking at the maintenance jobs, found all jobs completed successfully and without issues.  However, upon looking at the database’s statics it states no backups completed. Because…