Whether you are on a VPN or Proxy, that browsing data has to reach your computer, so the University router, (or whatever method they use for their networking), will know the destination.
"VPNs typically require remote users of the network to be authenticated, and often secure data with encryption technologies to prevent disclosure of private information to unauthorized parties."
So, your ID may be hidden from the internet servers where you obtain your data from, but not from the University servers where the data is routed through. It has to be that way otherwise the University servers wouldn't know where to send the data to.
My question should be pretty simple. I'm getting internet via the university provided network. I'm curious if my VPN (OpenVPN) will allow me to browse anonymously. As I understand it my IP address is changed to one in Netherlands, which I believe is where my traffic is being funneled. My question is am I visible because I am registered to access the internet via my user name and not my IP address.