Is it possible that during the action "Discovery -> Operation -> Add Host" that you can specify a none DNS value??
Perhaps being able to specify a zabbix agent key value like agent.hostname will work. We currently do not add our domain name "example.com" to our zabbix host entries and during the Discovery process it creates the entry with the full FQDN "server1.example.com".
With this we have to manually go into Zabbix and change this value as polling does not occur as we have the "Hostname" value in the agent configuration populated with just the hostname and not the FQDN name.
Agent Config Example: