Upon running screen with the -L flag, a file called 'screenlog.0' is created and all output written to it (which is great), but I will be running several screen sessions and I need to identify the logs with a unique number. Is it possible to change the log name?
You can edit your .screenrc file and add something like this
logfile /tmp/myownlog
Edit: already answered: https://serverfault.com/questions/248193/specifying-a-log-name-for-screen-output-without-relying-on-screenrc
Probably the easiest way is to use the following:
screen -L -Logfile log_filename your_command
Alternatively, there's a way to do it online.
Enter command mode in screen via Ctrl+a, : and use the logfile command with the name of the file you want as argument, eg: logfile whatevernameyoulike.log
Source: screen man page
Use script command inside your screen session.
来源：https://stackoverflow.com/questions/15026184/is-it-possible-to-name-the-screen-logfile-from-the-l-flag