Monuments to the Ku Klux Klan should be purged entirely:

In 2015, as Black Lives Matter gained prominence as a national movement, trustees were impelled to act. Students held protests and demanded that Saunders Hall be renamed Hurston Hall in honor of the celebrated author Zora Neale Hurston, who is said to have attended classes at the university. The vote to rename the hall was not unanimous.

But after a review, the trustees conceded that university leaders in 1920 made a mistake in citing Mr. Saunders’s role as head of the K.K.K. in North Carolina as a qualification.

That last sentence is a doozie. But it also brings up an important question, that may have some bearing on how other buildings are evaluated: If the KKK had not been mentioned in that document, would they still have renamed the building? Or was that particular acknowledgment just too blatant for the Trustees to ignore? There are numerous other historical sources verifying that Saunders was at least one of the Grand Poo-Bahs of the Klan back then; hopefully that would have been enough to strike his name, because there are likely other situations where there isn't a boldly typed sentence to rely on. Here's some historical context:

After the war, William Saunders and fellow Conservatives (later, they called themselves Democrats) watched with mounting anger as pro-Union whites, former slaves, and American Indians formed a political alliance within the state’s newly-established Republican Party. In 1868, that coalition crafted a new state constitution that granted all men the right to vote, regardless of race, and for the first time in North Carolina’s history mandated a statewide system of public schools. On Election Day, voters ratified the constitution and rewarded Republican candidates with both the governor’s office and control of the state legislature.

William Saunders and other Conservative leaders organized local bands of the Ku Klux Klan to reverse this political revolution. They found support among men who were struggling to recover from the devastation of war and feared losing the racial privilege that slavery had afforded even the poorest whites.

Klansmen perpetrated a reign of terror. In Graham, they lynched Wyatt Outlaw, a black constable, and hung his body from a tree in the center of town. In Yanceyville, they murdered state senator John Walter Stephens, a white Republican, and left his body on a woodpile in the county courthouse.

Klan violence frightened large numbers of voters from the polls and enabled conservative Democrats to regain control of the state legislature. In 1871, they impeached and removed from office Republican governor William Woods Holden, who had attempted to suppress the Klan. Democrats celebrated victory over what they called the “unwise doctrine of universal equality.”

The (new) Trustees made the right decision in changing the name of this particular building, but frankly, their reaction at being forced to do this makes me want to smack them on the back of the head instead of patting them on the back. From the OP:

Unlike at other universities, the trustees at Chapel Hill enacted a 16-year moratorium on further name changes. U.N.C. students continue to protest controversial figures, though. Last year they toppled a statue of “Silent Sam,” a Confederate monument.

Cecelia Moore, a historian and project manager of the task force on Chapel Hill’s history, said the moratorium was agreed to because it “would take years to develop methods” to best explain the university’s history. She said her task force was charged with providing information, not implementing policy.

“We need to give the university time to better tell the history and contextualize events,” she said.

The University has had 150 years to contemplate the ramifications of the Confederacy, and 100 years to contemplate the institution's culpability in normalizing Jim Crow developments. That 16-year moratorium serves one purpose alone, the guarantee that current Trustees won't have to deal with the hassle. And that is nothing of which to be proud.