Answer by DarkNeuron for Write to syslog from the command line

As a dev, I rarely have time to closely study man pages, so TLDR:

logger -p local0.notice -t ${0##*/}[$$] Hello world

The gibberish in the middle will translate to the calling program. So if you check the bottom of syslog you'll see something like:

May 07 08:27:14 ip-10-1-11-166 -bash[42108]: Hello world