Zend certified PHP/Magento developer

How can a site’s admins know who you are when you’re behind a proxy? [closed]

I recently got a life ban from Reddit for trolling a lot. I then made a new account but they banned that one the next day, sending a message with something like “every account you make will be suspended due to constant violation of our terms of service. Once I realized how bad it was, So I figured I was probably gonna need to use a proxy if I want to post on reddit from now on. So I set a proxy, tested my IP and whatnot before I signed up with a new account, but then I got banned AGAIN before I even did anything wrong. How did they do this? How did they know it was me? I never logged in with my two banned accounts while the proxy was on.

However they knew, I know its because of something technical because when I was trying to find a working proxy I kept refreshing the site, then when I found one it told me they have been getting too much requests from my computer and I had to wait like 10 minutes before I could sign up.

I’ve considered using a VPN, but if they can see through a proxy, I’m guessing a VPN wouldn’t solve the problem?