"Really anonymous" might be to set up a trust, interact through a lawyer, where MIT receives no information about the person behind the scenes.
But people at MIT knew, and it helped him make connections with other people.
In addition, the donations were reciprocated. One example (going from memory, so might have details wrong) was that one of the labs was asked to make a gift for Epstein.
Basically, once his reputation was in tatters following his conviction, the Media Lab and various individuals found it profitable to rent their reputations (and MIT's) to Epstein.
> Epstein had been supplying me the phone numbers of important scientists and financiers and media figures. “Do you understand what an extraordinary group of people they are, what they have accomplished in their fields?"