Logging Configuration in LTM HA

Logging is set on each appiance as its own configuration, however since most log alerts should be comming from the dataplane -only the active will be logging that traffic.  In your logging engine you should be able to search by name or IP -to ensure that the logs are comming in from both devices.

Depending on what interface you are logging from - and or how much natting - and proxy'ing you do - you should probably consider adding the IP address that logging is coming from under local IP - in the logging configuration.  
If the IP address in local IP  -is set in DNS , it should show up in the logging with the correct host name.