Logging syslog facility and priority
On RHEL 5, logging the syslog facility and priority is possible beginning with sysklogd 1.4.1-40.
From the package changelog:
* Wed Jun 20 2007 Peter Vrabec <firstname.lastname@example.org> - 1.4.1-40 - enable sysklogd to include priority/facility in message Resolves: #223573
-S Verbose logging. If specified once, the numeric facility and priority are logged with each locally-written message. If speci- fied more than once, the names of the facility and priority are logged with each locally-written message.
Add -S or -SS to SYSLOGD_OPTIONS in /etc/sysconfig/syslog and restart the syslog service for the change to take effect.
RHEL 4 and earlier
The provided sysklogd package does not appear to provide this capability.