Merely suggesting that you and the college girl have no blame for the critter’s former name. So the former name should not be polluting your relationship with the dog or with the college girl.
I would imagine that surrendering a dog to a shelter comes with some sort of “I give up all rights and privileges to said dog” type clause in the paperwork you sign. And while I haven’t gone and dug up all the paperwork for our rescue dog, I don’t recall anything saying that the previous owners have any sort of rights or ownership to exercise.
Considering the reasons why some creatures wind up in shelters, I’d expect that in some cases the previous humans would be forbidden to take them back.
I think some shelters require adopters to agree to return to the shelter rather than rehome elsewhere if they ever can’t keep the pet, though.