https://www.rsyslog.com/
Run Rsyslog instead of Syslogd
Syslogd has a couple of quirks, e.g. it does not add its hostname / IP to the syslog information.
Rsyslog is the standard in the Linux world, and it's available in the OpenBSD ports as well via the package manager.
pkg_add rsyslog rcctl disable syslogd rcctl enable rsyslogd /etc/rc.d/rsyslogd start
Then just configure Rsyslog.