Citing Facebook’s mishandling of user privacy and its use of an opposition research firm to discredit critics, San Francisco Supervisor Aaron Peskin is pushing to remove Mark Zuckerberg’s name from the city’s public hospital.

The hospital was renamed Priscilla Chan and Mark Zuckerberg San Francisco General Hospital in 2015 after the Facebook CEO and his wife contributed $75 million to the hospital’s foundation.

Peskin on Tuesday asked the city attorney to outline a procedure for removing Zuckerberg’s name from the hospital. (Though it formally bears Chan’s name, the hospital often calls itself just “Zuckerberg San Francisco General Hospital and Trauma Center” in signage.) In his remarks, Peskin cited the Cambridge Analytica scandal — in which the political data firm obtained the personal information of as many as 87 million Facebook users without their consent — and revelations in a recent New York Times article about Facebook’s hiring of a political consulting firm to discredit activists critical of the company. The social network, according to the Times, sought to cast some criticism of Facebook as anti-Semitic, while Facebook’s consulting firm was also accused of tactics tainted with anti-Semitism.

“It is not normal for private entities to use that information to spread, and in this case anti-Semitic, conspiracy theories on platforms they control,” Peskin said at Tuesday’s Board of Supervisors meeting. “It is not normal for Mark Zuckerberg and (Facebook chief operating officer) Sheryl Sandberg to refuse to accept responsibility and to publicly distance themselves from acts that they have personally instigated. ... This is about the integrity of institutions and spaces that are overwhelmingly funded by public money and taxpayer dollars.”

A spokesman for City Attorney Dennis Herrera said the office has received the request to look into the matter and does not have a policy position on the issue.

The city has moved to rename some public structures before, such as Justin Herman Plaza on the Embarcadero, but removing Zuckerberg’s name from the hospital may trigger a dispute because of a naming agreement Zuckerberg and Chan reached with the hospital, which is owned and operated by the San Francisco Department of Public Health. The agreement, adopted by the Board of Supervisors in 2015, says the hospital is to be named the Priscilla Chan and Mark Zuckerberg San Francisco General Hospital and Trauma Center for 50 years. The $75 million gift is believed to be the single largest contribution by private individuals in support of a public hospital in the United States.

“It is customary in hospital capital campaigns to provide naming opportunities in honor of major philanthropic gifts, as a critical strategy for raising awareness for the project within the community and for garnering action from other community members and philanthropists,” the resolution said.

The resolution does not explicitly address what would happen if the naming were revoked. When asked whether the hospital, if the city were to seek to remove Zuckerberg’s name, would have to give the money back, a hospital spokesman said he “couldn’t offer an opinion on that.”

Zuckerberg San Francisco General Hospital is the only public acute-care hospital in the city, serving about 108,000 people each year. Chan, Zuckerberg’s wife, previously worked there as a pediatrician.

Facebook did not respond to a request for comment.

In a written statement, hospital CEO Susan Ehrlich said the contributions from Zuckerberg and Chan have helped the hospital acquire new technology to serve patients, renovate the building and improve patient care.

“In acknowledgment and appreciation of that gift, our hospital now carries their names,” Ehrlich said. “Naming is an important convention in philanthropy that encourages additional donors. ... We are honored that Dr. Chan and Mr. Zuckerberg thought highly enough of our hospital and staff, and the health of San Franciscans, to donate their resources to our mission.”

Peskin’s move comes after nurses at the hospital protested the Zuckerberg name, expressing similar objections.

There is precedent for sports stadiums being rebranded after their corporate namesakes imploded: Houston’s Major League Baseball stadium went from Enron Field to Minute Maid Park after massive fraud at the energy company came to light.

“You can have situations where you look at the individual in the company and say, ‘Well, who wouldn’t take the money from this four-star company and they’re involved in saving people’s lives?’” said Andy Dolich, a former Oakland A’s executive who runs a sports consultancy. “It’s a perfect match, until it isn’t.”

Catherine Ho is a San Francisco Chronicle staff writer. Email: cho@sfchronicle.com

Twitter: @Cat_Ho