Saving files with layer name

Hi

I have a PS file I need to version out to 7 versions of about 45 variations. I have all the layers and groups named so it makes sense and it occurs to me that the correct name for the outputted jpegs would actually be the same name as the current layer.

Does anyone know a way, either with actions or batch automate, to save a file using the currently selected layer as the file name? The file naming options in batch seem really limited.

TIA

Bettsy