For older versions of gnu-screen (i.e. without the %S), I found out how to print the session-name in the hardstatus or caption of gnu-screen by reading this answer.
The solution is to add the following lines to your .screenrc:
hardstatus string '%H:%`'
backtick 0 30 30 sh -c 'screen -ls | grep --color=no -o "$PPID[^[:space:]]*"'
How do you append text after the session-name prints?