You could add a final $project stage to rename the fields if you wanted to.
There’s probably a better solution out there that I’m too tired to see right now, but the above will give you something to play around with.
As always, this query works, but may not be efficient at higher amounts of data. Always test in your environment with production level data to see how it works for you. Filter out as as much as you can early in the pipeline so you don’t do unnecessary work in the pipeline.