How do I use Nagios to monitor a log file that generates a random ID
Solution 1:
I would run a separate script, via cron, that identifies the newest log file and makes a symlink to it (named something like "latest.log"). There are several ways you could do this (using ls -rt | tail or find -mtime, for example).
If the new logfile is created at the same time every day, schedule it to run right after that. If not, have it run every (minute, 5 minutes, whatever), checking for a new log file.
... And then have check_logfiles use that symlink.