As you might guess, he lent his name to the state university in New Jersey (formerly known as Queen's College), which adopted the title "Rutgers" in gratitude for his support, which allowed it to reopen after the Revolutionary War. It wasn't the only thing to be named for him: both Henry Street and Rutgers Street in Manhattan are taken from his name, as is the Rutgers Presbyterian Church - even though Rutgers himself was Dutch Reformed (the reason being that Rutgers' gifts to the Dutch and other churches lapsed before they could fulfill his condition of building a church on time).
Rutgers could afford to be a major philanthropist; his family had been in the country since 1645, when they settled at the Dutch outpost of Fort Orange (now Albany). He was also a lifelong bachelor without any immediately family. King's College Alumni euphemizes his situation by noting that "it seems he never engaged in any business, but found his time sufficiently occupied in the care of his estate". It goes on to say that "there is scarcely a benevolent object or humane institution which he did not liberally assist. He relieved the poor individually and supported deserving young men". He even "had a kindly expression," which is a curious thing for a book written 80 years after his death and based on official state biographical sketches to say. Indeed, not everything Rutgers did with his effortlessly gained family money turned out to be so noble - he also supplied the funds for the construction of the first Tammany Hall.