Debian is different from Slackware, in a few mainor ways. Here is a list of what I didn't forget.
In slackware, it's /etc/HOSTNAME, in Debian it's /etc/hostname.
I've just noticed that I only put "trix", not the fully qualified hostname. trix is a unique alias in /etc/hosts, maybe that's why it works.
The file is used by /etc/init.d/boot, as a parameter to the hostname command. After that, the hostname command returns the systems name. Some programs read /etc/hostname, because they know it's there, and it's easier to read a file, than start up a new process.
If you change this file, you change the name of the system (after next restart).