One way to do this would be to create a custom workflow launcher to listen to the uploads under your project path and as soon as an upload happens you can re-write the file name, but make sure it doesn't conflict with the DAM Update Asset Workflows.
As Veena mentioned use Custom workflow to change the name of asset. which will change the name of the asset.
Just adding on to that ,you can disable the Update Asset workflow for a while while uploading the asset once the asset got uploaded you can enable it. This is for avoiding conflict with Update Asset workflow.
You can call "update Asset workflow" from your own custom workflow model, after the step where you are changing the name of asset.
For already uploaded assets you can write groovy script to append the BU in your aseets