Why is my site showing up on someone else's domain?

The answer to this question is almost always that this domain is directed to your server. It does not depend on your server or your billing account.
Web servers are organized in such a way that in the absence of the requested host in the config read the config of the first domain on the same IP.
 
Is it possible to prohibit the display of "left" sites from your server?
Yes, of course. To do this, please contact technical support by creating a ticket.
We will check what is really the reason and if it is the situation described above, we will adjust your web server config to disallow such domains.