There's no way to hide this info, but would you consider network access or firewall rules that would prevent them from accessing the database when not on the client server?
Also, you could enable database auditing to keep an eye on what they're doing - if they're that precocious, every student should get their own user, so you know who is doing what.
What do you think they're going to do? If they can break something by knowing your server name/port then you should really be questioning your security anyway.
The more you try and do things like this, the more students will see it as a challenge to get around it.