Hi,
I’m using a dedicated server and I’ve just noticed someone using their domain but showing my website.
Is there a way in the server logs or whatever that would show any abuse of such a thing?
Yes there should, if there’s a control panel like cPanel installed on the server check the access logs. If they use any content on your server [1] you would be able to see it and [2] also able to lock them out quite easily. Just make sure your domain is the only domain in the ‘hotlink protect images’ section of cPanel.
But that’s cPanel, I am sure if you have no (or any other) control panel your dedicated server provider is able to help you out.