Display Lister name in the toolbar

Is there a way to display the currently open Lister in the toolbar?

Not in the toolbar, but you can display it in the titlebar, if you mean the layout name.

Yes, I would like to display the layout name of the opened Lister layout in the titlebar. How can I do that please?

There's checkbox at the bottom of Preferences / Display / Options:

  • Display layout name (if any)

If you are looking for more options this addon script might be of interest.