My question is why are you renaming them? Even if you feel the need to rename them why are you removing the original file name?
Each camera has its own unique file naming which with every camera I have worked with, in the case you have 2 cameras exactly the same, you can change the naming in the camera to separate them.
I find the easiest way to tell which shot was taken by which cameras is by the file name the camera gives to the image. Even when I had 2 identical cameras I never renamed the files on import. I changed the file name the camera gave to the file in the camera. One started with a 1 and the other started with a 2.
I'm renaming them to reflect the date of the shoot and the subject's name.
I think I figured it out, I had to change my previous "custom rename" to rename to shoot name + sequence