The default installation comes with no syslog daemon, there are different implementations available.

socklog is the implementation from the runit(8) author and Void Linux provides a package with some basic configuration for it, this makes it a good choice if you don't know which one to choose.

# xbps-install -S socklog-void
# usermod -aG socklog <your username>
# ln -s /etc/sv/socklog-unix /var/service/
# ln -s /etc/sv/nanoklogd /var/service/

Other syslog implementations like rsyslog and metalog are available in the package repository too.