I assume debian package should work out of the box, but found the following issue:

Package use zabbix_agent.conf provided by upstream, and there Hostname variable set to "Zabbix Server".
When I install zabbix on multiple servers, this force me to change this value on every host.

But if you let this variable unspecified it's default value will be equivalent to server's hostname.

This issue was reported on debian bugtracker: http://bugs.debian.org/cgi-bin/bugreport.cgi?bug=727604

Dmitry suggests that this should be fixed upstream. So I forward this issue here.