Change default background layer to original file name

That was perfect! Thanks! Is it possible to add "lock layer" step to the end of that script? 

You can convert  a background layer to a normal layer and name it anyway you want.  All PSD do not have a background layer.  The background layer is special bottom layer and one is not required.   You can script the process even make an open event handler. But you need to handle what you want to do when there is no background layer. You will be making all PSD to not have as background layer you will most likely open these also and If you save the PSD with a new file name will you also be renaming the bottom layer. Save even handlers are triggered after the save completes the rename can not be done by  a save even handler the documen may not longer be in Photoshop. The open event handler  can rename a bottom normal layer.  The open event handler would need to be a script so it can use logic to determine what kind of layer the bottom layer is in  a PSD file and be able to retrieve the backing file name and file type,