Steps involved in configuring SQL Server and its components after server is renamed
You've noted that your setup doesn't use mirroring, failover clustering, replication, etc, so it sounds like you've done everything you need to do inside SQL Server.  If you are changing the name of the this server as part of replacing an old decommissioned server, you'll need to ensure the logins from the old server are configured in the new server to ensure clients will be able to connect.  

As for Reporting Services, aside from altering the Database settings, you'll also need to change the name of the Report Server URL in the &lt;UrlString&gt; node of the RsReportServer.config in %SystemRoot%\Program Files\Microsoft SQL Server\&lt;SSRSInstanceName&gt;\Reporting Services\ReportServer.  Ensure the UrlString points to the correct name of the server, then restart the SSRS service.

You'll need to change the Report Server Database to refer to the new name of the SQL Server machine:



It's not clear what the actual problem is regarding your scale-out deployment.  Perhaps a screenshot of the problem screen might help explain what you're seeing.