You can use VMware Syslog Collector and as I know, it will write messages to separate files for each ESxi server.
Configuring syslog on ESXi (2003322) | VMware KB
Also you can use Linux as syslog server, here is an example for:
You can use VMware Syslog Collector and as I know, it will write messages to separate files for each ESxi server.
Configuring syslog on ESXi (2003322) | VMware KB
Also you can use Linux as syslog server, here is an example for: