Whether this is visible to the outside world depends on what kind of firewall your university network uses.
You could try using the tools at www.whatismyip.com to see some of what's being exposed to the public Internet. The basic info at the home page will show you what public IP you have; you can compare this with the configuration of your PC to see if they're the same (the PC may have a private IP, and the public IP is is the address of the university's firewall).
If your internal IP is being exposed, the university may still be using split DNS to provide different name resolution internally and publicly. Use the Reverse DNS Lookup tool to see what name is being exposed to the public. I expect it will be a generic name derived automatically from the IP, not the one with your name in it.
Also, it's possible that the university uses dynamic address assignment that doesn't associate a specific IP with your PC permanently. Each time you connect to the network you may get a different IP. So if some outside site has your IP saved, and tries to look up the name later, they may get someone else's name because the assignment has changed. The "Last login" message you see in the login greeting on your server isn't affected by this because it saves the name when you login, not the IP.