Q: can I combine my Apple Tv purchased movies with my private collection

no you can't combine Apple Purchased movies with your "private collection" if they were home movies, DVD "rips" or purchased from another provider (e.g. Microsoft, Disney, VUDU, etc.)

Combine in what way?

Your Purchases made on an Apple TV can be made part of your iTunes library on your computer where I assume your private collection is.

You can download the movies to the computer by going to the Purchased section in iTunes.

Download your past purchases - Apple Support

You can put them together in iTunes and view them via home sharing through the computer app. If you designate them as movies they will be listed with your purchased movies, which is good if your private collection is (say) TV recordings you have made yourself. If your private collection is home videos, you can designate them as home videos so they get separated from your purchased movies whilst still being accessible through the computer app.

As I said previously, you CAN combine your private (or non-purchased) content