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 a
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, for example:
logfile whatevernameyoulike.log
Source: Screen man page
Probably the easiest way is to use the following:
screen -L -Logfile log_filename your_command
You can edit your .screenrc
file and add something like this:
logfile /tmp/myownlog
It is also answered at Specifying a log name for screen output without relying on .screenrc.