Auto populate List Column

I want to auto populate a Column that's in all my document libraries.  I want to set this Column to the document library name.

I know I can create an ItemAdding Event Receiver to grab ListTitle. 

But my situation wouldn't be based on an event.  I only want to run this once to populate this Column, then it will never change.

I would have to be based it on a WorkflowStarted.  But in the WorkflowStarted Event Receiver, I don't see how to grab ListTitle.

Does anyone know how to grab ListTitle in the WorkflowStarted Event Receiver?

Or do you know of another way to grab ListTitle and populate a Column with that value?

thanks!