How to avoid changing the backdrop of my neighbor's chromecast?

I'd like to set my Chromecast's backdrop up with some custom pictures, but any attempt to do this also changes the pictures on my neighbor's Chromecast. We don't have a problem here - we had a good laugh about it - but is there any way to change the backdrop of my Chromecast and not theirs? The two seem to be linked in the Android app.