To receive logs from other hosts we can set up rsyslog to receive logs from other hosts. It's been explained in various ways various sites, which is a bit confusing so here is one that is most straightforward and works for me, as simply put as possible. This is an UDP setup and it is done with CentOS / RHEL 7.

Note that this adds logging per host (including localhost) under /var/log/remote in addition to your existing logging so it will increase your log partition usage. If you want to replace the existing logs with this solution you must apply a stop rule at the /etc/rsyslog.conf. I did not explore that so if you do please leave a message here so I can update this guide accordingly.

Make a directory and relabel (selinux) it for syslog use

mkdir /var/log/remote
chcon --reference /var/log /var/log/remote

Edit /etc/rsyslog.conf so that before UDP syslog configuration you add this new template configuration:

$template RemoteLog, "/var/log/remote/%HOSTNAME%/%programname%.log"
*.* -?RemoteLog

After which you uncomment the UDP syslog reception lines:

$ModLoad imudp
$UDPServerRun 514

Open UDP port 514 to the hosts you want to receive log from. I use iptables so I added this line to /etc/sysconfig/iptables

-A INPUT -p udp -m udp --dport 514 -s 192.168.120.0/24 -j ACCEPT

After which reload iptables with

systemctl restart rsyslog

Restart rsyslog

systemctl restart rsyslog

And you should start getting /var/log/remote/<hostname> directories under which the log files appear.

All comments and corrections are welcome.