[Hans]

I think you have to make a small modification within your /etc/postfix/main.cf.
So here is my suggestion:

Replace the line:
mydestination = host.mydomain.com, localhost.mydomain.com, localhost.localdomain, localhost

with:
#mydestination = host.mydomain.com, localhost.mydomain.com, localhost.localdomain, localhost

And add the line:
mydestination = /etc/postfix/local-host-names

Restart postfix afterwards by executing:
/etc/init.d/postfix restart