unusual activity on my apple tv. Someone is renting and purchasing films on my account

This is primarily a user-to-user support forum; other Apple users like you. We don't have access to information about charges to your account. See each of the steps in the following instructions, including information about changing your password. They also include information on contacting Apple Support if the other steps don't help: If you see 'apple.com/bill' on your billing statement - Apple Support

Check the list of devices where your Apple ID account is used, see if you can account for all of them:

Check your Apple ID device list to see where you're signed in - Apple Support

Change your account password to lock out unauthorized users (= everyone but yourself):

Change your Apple ID password - Apple Support

Keep your Apple ID account credentials secure:

Security and your Apple ID - Apple Support

Notable is two-factor authentication, which notifies you if your account is being used on a new device.

Are these mystery charges listed in your purchase history?

See your purchase history for the App Store, iTunes Store, and more - Apple Support

You may also want to take a look at this article: If you think your Apple ID has been compromised - Apple Support

these mystery [charges] are appearing in my purchase history but I did not rent or purchase [them]. I am not getting a receipt from apple for these purchases whereas I do get a receipt for genuine purchases

If no-one else has access to your Apple ID’s email account to delete specific invoices, then you may want to contact Apple Support about the missing invoices.