But decisions by major institutions to remove the Sackler name from existing facilities have been rare. This year, the Louvre in Paris removed the name from a wing that had been known since 1997 as the Sackler Wing of Oriental Antiquities. In that case, however, the Louvre said that its naming agreements lasted only 20 years.

There were three Sackler brothers, all of whom made gifts to Tufts, and different branches of the family have responded differently to Tufts’s decision.

One of the brothers, Arthur, is widely credited with shaping modern medical advertising, but he died before OxyContin was introduced and his brothers then bought his stake in the company. His widow, Jillian Sackler, released a statement emphasizing that her husband had no involvement with OxyContin, saying, “It deeply saddens me to witness Arthur being blamed for actions taken by his brothers and other OxySacklers.”

Michael Ward Stout, a lawyer who has worked with museums, said that an institution’s right to withdraw from a naming agreement depended on the terms of the contract. He said that when Lincoln Center in New York wanted to change the name of Avery Fisher Hall, the home of the New York Philharmonic, to attract a major gift for its renovation, officials paid the Fisher family $15 million for permission to drop the name. (Mr. Fisher’s original gift to support the hall, in 1973, had been $10 million.)

In some cases, like that one, “You can buy yourself out of it,” he said.

In 2018, the Massachusetts attorney general filed a civil complaint against eight members of the Sackler family, along with Purdue and numerous Purdue executives and directors, saying that the company had misled doctors and patients about the risks of OxyContin.

In a court filing this past January, the attorney general asserted that the Sacklers and Purdue had used their relationship with Tufts to promote use of OxyContin by gaining access to local doctors and trying to influence research about pain treatment.