Unfortunately no. The purpose of an alt tag is to describe your image in case it doesn't load. And while something could possibly be written to insert the image name as the alt tag, it really is not descriptive and does not serve a purpose.
as I don't use the alt tag option as it is usually my last on my list is to tag everything when the website is complete.
I used to have the same workflow and adding alt to images at the end was a pain.
Now I have Edit > Preferences > Accessibility, Images checked and DW prompts me to insert the alt attribute every time I insert an image.
I've decided it's best to be forced to do it as I go rather than revisit the images when my design is done.