Name a Byobu session?

Is there a way to create identifiable Byobu sessions so that when I've got multiple sessions running, the byobu-select-session menu gives me a list of sessions I can recognize, as opposed to non-descript tmux port numbers?

In an ideal world, it would be great to be able to both start a session giving it a name and to modify such a session to change a name if it's already running? Is this possible, how?

Edit 1: Some further details:

• I'm using tmux as the backend and don't especially want to switch back to screen.
• I've now tried starting a session with byobu -S "Name" to no avail :-(

Edit 2: Some discoveries:

• I've now discovered a partial answer in using tmux native commands: tmux rename-session <current-name> <new-name> renames an existing session and tmux new -s session_name creates a new names session. I'm surprised byobu -S "name" isn't liked to tmux new -s session_name for byobu with a tmux backend.

Byobu is simply a shell for the tmux (or screen) back end terminal multiplexor. You can therefore pass any command that your back end supports through Byobu.

Byobu with tmux back end

To start a new Byobu session with a specified name:

byobu new -s <session-name>

To change the name of a pre-existing session:

byobu rename -t <session-name> <new-session-name>

Byobu with screen back end

To start a new Byobu session with a specified name:

byobu -S <session-name>

To change the name of a pre-existing session:

byobu -X <session-name> <new-session-name>

Note: All credit to J.F.Sabastian for his help. I've now verified the above commands are correct for both Tmux and Screen backed Byobu.