The color lends itself to a few birds. Kestrels, flickers, swallows, bluebirds, robins, finches, crossbills, towhees, sparrows, orioles, blackbirds, tanagers, and grosbeaks all have species in New Jersey with orange coloration. Out of these, I believe the best nickname would be the Kestrels, as predatory birds are more common among team nicknames.
A believable name and backstory for a Paterson-based college would be Hamilton University, among the "Ivies" of the AHS Universe. From Wikipedia, "In 1791 Alexander Hamilton (1755/57–1804), first United States Secretary of the Treasury, helped found the Society for the Establishment of Useful Manufactures (S.U.M.), which helped encourage the harnessing of energy from the Great Falls of the Passaic River to secure economic independence from British manufacturers. The society founded Paterson, which became the cradle of the industrial revolution in America." This connection to Hamilton seems strong enough to justify the founding and naming of a university in his honor.