The most likely reason that you are not able to alter the filename is because you are not the project owner (aka the person who created the project).
If you need to change the filename and you are not the project owner, the only way to do this (other than contacting the project owner), is to:
Click on the image with the filename you need to change, and enter the comment and markup view
From your computer, drag and drop the same image but with the correct filename onto the image that's currently in VeryBusy (instead of dragging and dropping, you can use the upload button below the image)
The image and filename will be replaced with the image and filename you uploaded
If you are the project owner and you change the filename, you may wish to let your collaborators know. Depending on your workflow, they might need to update their files to reflect the same name in order to ensure the round counting system in VeryBusy continues tracking the image.