I'm forwarding all syslog events to papertrailapp.com, and they are identified as sent by
localhost. It's not convenient, since I have a few servers and all of them are
localhost-s. How can I configure syslog on every machine to have their own unique names?
You can fix that by setting the hostnames for these computers.
(r)Syslogd does not have a option to set a hostname to transmit/log-