Accessing names of the images being inferred by Batch Transform Job endpoint

I have used a custom container for Batch Transform inferencing.
Suppose an input file is named: "image_1.jpg", then I am getting the output for this image as: "image_1.jpg.out". And this happens for all the images present in the input S3 folder for Batch Transformation.

But now I have a requirement that I write the **name of the image** into the "image_1.jpg.out".
And a bonus task I have is to **change** the name of the file while writing it to S3.
How do I go about this?

I have implemented the inference pipeline by using the "[scikit_bring_your_own](https://github.com/awslabs/amazon-sagemaker-examples/tree/master/advanced_functionality/scikit_bring_your_own)" Jupyter Notebook. So I went through the "serve" and "predictor.py" files present in the "container" folder of the above-shared link. But I could not find the point where the Images were being read from S3 and the .out was written to S3.

Any inputs will be much appreciated.