Report Viewer gives 401 error if machine accessed under another name

I have a Server with an IIS application, SQL Server 2012 and Reporting Services.

The web application uses the report viewer to access the reports.

The server can be accessed under its own name,  a DNS alias,  and is published on the internet under yet another name.

If a report is accessed under its own name,   everything works fine.  But that is not the intention.

Under the DNS alias and on the internet we get an error:

The request failed with error 401 Unauthorized.

If I try to access the reports directly  with http://servername/reportserver  orhttp://servername/reports   it works fine  for all three the names.

The authentication part of rsreportserver.config says:

<Authentication>
  <AuthenticationTypes>
   <RSWindowsNTLM/>
  </AuthenticationTypes>
  <RSWindowsExtendedProtectionLevel>Off</RSWindowsExtendedProtectionLevel>
  <RSWindowsExtendedProtectionScenario>Proxy</RSWindowsExtendedProtectionScenario>
  <EnableAuthPersistence>true</EnableAuthPersistence>
 </Authentication>

If I look at the server with procmon,  I do see an access trial if I use the DNS alias or the internet adress.

On the previous machine with the same configuration (as far as I know)  it worked fine.

Does anybody have an idea,  how we can solve this?

Joachim.