If you had simply answered “Source”, I was planning on withdrawing quietly, as I have no experience with that.
If you had answered “Playlist”, I would have suggested that you try “Export All from Playlist”, which has a name generator in it.
I always have been Exporting from the Timeline (until I recently began to convert batches of raw and intermediate video from the Playlist). Shotcut has always provided me with a name; the name of the current project. (I always have a current saved ProjectName###.mlt, where ### is the sequential number of the edit checkpoint save)
When I am making test Exports, the name of a previous Export is available in the Export to… window that pops up; I select one, it asks “This video already exists, do you want to overwrite it Yes/No?”, I choose “No”, and now the name appears as the default on the Export filename line where you want it, ready for me to edit it.