screen -D -m starts a new session in a detached state without forking a new process. The command will not terminate until that new screen exits.
You can still put the command in the background with Ctrl+Z followed by
bg, and then check what name it got with
screen -ls (it will say
(Detatched) at the end and also mention the time it was created). The name is the first word on one of the lines and will likely contain some digits and your hostname.
Attach to the session with
screen -r name (where
name is the name shown by
screen -ls for the started session that you'd like to end) and exit from it.
You don't need to exit or detach from the original
screen session to do any of these things.