There is a "%S" variable for session name noted at the bottom of the Session's options Log File dialog. I think that will work for what you mean by "connection name"
You may also want to review these 2 threads which talk about setting a Logon script that will allow more specific log creation:
https://forums.vandyke.com/showthread.php?t=10506
https://forums.vandyke.com/showthread.php?t=3525