When my parents were living with me (temporarily) I had a Wyze cam on my end of the house (registered under my own account) and they had one on theirs (registered under their own account). I had access to theirs (they shared with me), but they did not have access to mine. After moving out and installing all Ring devices in their home, they gave me their Wyze cam. Instead of simply plugging it back in, I decided to add a new device within my account. I was able to do this and I gave it a new name. My question is: If my parents open the Wyze app on their phone, will they be able to see that camera? Or how will their old camera appear in their app? Will it no longer be available for them? This is a privacy question/issue because I don’t want them randomly spying on me.
Welcome to the Forum, @rachel5000! 
This post/topic may be instructive:
These should be the short answers to your questions:
Since you added it to your account as a new device (presumably did a factory reset and set it up as if for the first time), then that camera should be gone from their account.
It shouldn’t appear at all.
That’s my understanding, yes.
Here’s the caveat: The post I linked above sparked a long topic and a discussion that eventually led to Wyze reversing a policy/feature that they previously had whereby if a camera owner had a subscription (e.g., Cam Plus) and a camera was stolen and set up as new under the thief’s account, the camera owner would still have access to previously-saved cloud recordings for a couple of weeks. In other words, the camera owner would still be able to access recordings made while the camera was still in the owner’s possession. Wyze essentially reversed that policy/feature at some point—meaning that any cloud recordings were lost, along with the stolen camera—but then this summer announced that they would be reinstating it at some indefinite point in the future:
I haven’t seen any official word on when that might be.
This may all be kind of a moot point in your case, but it might be something you’d want to be aware of because it’s somewhat related. To your main point:
My understanding is that this should not be an issue because you added it to your account as if it was a new device.