While naming decisions are up to the university’s board of trustees (which includes Mr. Eisgruber), Mr. Eisgruber promised to push for removing a large mural of Wilson from the residential college’s dining room and to direct the trustees to survey “the campus community’s opinion” on the Wilson School name and then vote on it.

The protesters also called for mandatory courses on “the history of marginalized peoples,” for “cultural competency training” for the staff and the faculty and for the creation of dedicated housing and meeting space for those interested in black culture.

But as Princeton takes its turn in the national roll call of college campuses where long-festering issues of race have burst into the open, spurred by events in places like Ferguson, Mo., and Charleston, S.C., it is not surprising that the conversation would pivot around Wilson, an alumnus.

“In some ways, that’s the role that symbols play in American politics and culture,” Mr. Eisgruber said in a phone interview on Sunday before sending an email addressing the issue to the university community. “People become very invested in symbols. And one of the benefits of having a genuine public discussion, informed by scholarly opinion, about some of these questions is that it can help educate people about problems that go beyond the symbol in our society.”

In the wake of the sit-in, students were divided on the renaming; even many sympathetic to the Black Justice League’s other demands said that expunging Wilson’s name went too far, or was unlikely to serve a constructive purpose, or both.

A counterpetition circulating on Change.org called the proposal a “dangerous precedent” for future students who “seek to purge the past of those who fail to live up to modern standards of morality,” as well as a bid to erase Wilson’s positive contributions.

Image Thomas Woodrow Wilson in 1903, when he was president of Princeton University. Credit... Universal History Archive/Getty Images

But one Black Justice League member, Wilglory Tanjong, rejected that argument.

“We don’t want Woodrow Wilson’s legacy to be erased,” said Ms. Tanjong, a sophomore who was born in Cameroon and grew up near Washington. “We think it is extremely important that we understand our history of this campus. But we think that you can definitely understand your history without idolizing or turning Wilson into some kind of god, which is essentially what they’ve done.”