In the autumn of 1954, four months after the Supreme Court outlawed segregation in District of Columbia public schools in a companion case to Brown v Board of Education, six of the city's seven all-white high schools accepted black students for the first time, from a handful to hundreds. The seventh was Woodrow Wilson High School.

Wilson had been named by Look magazine as one of the ten best high schools in America a few years earlier. Its student body boasted the children of diplomats and congressmen; graduates included future senator John Warner, future anchorman Roger Mudd, future billionaire Warren Buffett and future Aids activist Larry Kramer. But as the rest of Washington began grappling with desegregation — hundreds of white students at other high schools staged a three-day walkout that October — Wilson's 1,143 students, 62 faculty members and staff remained entirely white.

Today, Wilson is DC's most diverse public high school: 39 per cent white, 29 per cent black and 22 per cent Latino. It has long considered itself progressive. In the 1960s, Wilson students protested the war in Vietnam. In the 1980s, Black Power organiser Kwame Ture, formerly Stokely Carmichael, visited an English class. In 2014, students outnumbered and outchanted antigay hatemongers from Westboro Baptist Church who picketed after the school's principal at the time came out as gay. Wilson has a diversity task force, gender-neutral bathroom signs, and clubs with names such as Common Ground and Gender Sexuality Alliance.

But since before its doors opened in 1935 — to white students only — Wilson has been defined by race. It was built across the street from a black neighbourhood, Reno City, which was at the time being slowly demolished by the Federal Government. And it was named for a president who wrote sympathetically of the Confederacy and Ku Klux Klan, resegregated federal agencies and screened The Birth of a Nation at the White House. Wilson's beliefs weren't unknown inside the building. In 1972, an African-American sociology teacher, Edward Cannon, told the student newspaper that the school was named after "a bigot". Wilson was "founded in racism" Cannon said, "and the odour still exists".

Amid the nationwide protests for social justice, cities and states have been reckoning with the names of public institutions. Who should be defrocked and why? How should they be replaced? In DC, a committee reporting to the mayor, Muriel E. Bowser, proposed this summer renaming dozens of schools, parks, playgrounds and buildings. Top of the list was Wilson, where changing the school's name already had spurred a coalition, a public forum, a petition and protest rallies. A non-binding online survey of replacement candidates ended this month, and Bowser and DC Public Schools chancellor Lewis D. Ferebee are expected to announce a new name, which would need approval from the DC Council, in coming days.

Six of the seven finalists are black educators, politicians or literary figures. The other is purely geographic: northwest. Four-term DC mayor Marion Barry Jr was a polarising figure in life, and he just had a city government building named for him. Pulitzer Prize-winning playwright August Wilson would appease alumni attached to the surname, but has no personal connection to DC. A Wilson parent who was involved in the name-change effort, Zerline Hughes Spruill, who is black, said Bowser "put ‛Black Lives Matter’ on the street in front of the White House. I'd like to think she wouldn't put ‛Wilson' back on the name of the school".

Any change will be a historical corrective. "Everything Wilson did was to undercut the very people whose descendants now go to the school," said Chris Myers Asch, the coauthor of Chocolate City: A History of Race and Democracy in the Nation's Capital and a 1990 Wilson graduate. But only one namesake would fully confront the century of racial ignominy that has helped define the school: a teacher named Edna Burke Jackson.

After the Supreme Court ruling in 1954, the demographics of working and middle-class Washington shifted. White families packed up for Maryland and Virginia, and DC’s population flipped — from 65 per cent white in 1950 to majority-black in 1960. Although the wealthier neighbourhoods that fed into Wilson didn’t change, the school system sought to look as if it was proactively desegregating the school. On September 12, 1955, Wilson enrolled its first black students, one boy and one girl, both in the tenth grade. "Wilson High Integrated", the Washington Evening Star reported. The school also was assigned two black faculty — chemistry teacher Archie Lucas and Jackson, who taught European and world history.

Jackson graduated in 1928 from Dunbar, the legendary black DC public high school, where she was a stalwart of the debate team, editor-in-chief of the newspaper and a member of the French and Latin clubs. She won a scholarship to Howard University, studied French and history, and earned a master's in education. Today, she might have become a lawyer or a diplomat. Then, she did what many highly educated black women did: she taught. After six years at a black high school in Tulsa, Jackson returned home in 1940 to work at DC’s Cardozo High School, which was also all-black. Fifteen years later, she was sent to Wilson, where she would stay until retiring in 1976.

Her first years there couldn't have been easy. In his memoir, Ghost Light, the writer Frank Rich, Wilson Class of 1967, recalled a history teacher who asked students to petition Congress to change the national anthem to Dixie. Former students and a family member told me that white teachers wouldn’t sit with Jackson at lunch and used the n-word in her presence. "It's certainly not the era where you would stand up and create some sort of huge thing about it," Sue E. Houchins, an African-American studies professor at Bates College who was a close family friend of Jackson's, told me. "You moved yourself through it with dignity, and that is who she was."

Washington was a government town but a Southern city. Homes around Wilson were built with restrictive racial covenants attached to their deeds. "Make no mistake, the class was full of children of racists," one alumnus commented in the name-change survey. "[Jackson's] even temper and intelligence in the face of these students have been a lesson for life."

Former students said Jackson, who died in 2004, was kind, even-tempered and serious, and held her students to high standards. "She was all about education," her niece, Paula B. Duckett, told me. In the late 1950s, after a lesson on Communism and the Cold War, Jackson arranged for her class to visit the Soviet Embassy. "She insisted that in order to defend democracy, Americans must know freedom's enemies," a student from the early 1960s wrote in the survey. Leland Barrows, a retired professor who graduated from Wilson in 1960, told me he became a historian in part because of Jackson: "She viewed the study of history as a search for truth."

In DC's first public outreach about a new Wilson name, I nominated Reno City to amplify the historical truth of what was destroyed across from where the school now stands. That name didn't make the cut, and when the final round began, I voted for Vincent E. Reed, Wilson's first black principal, who was dispatched to the school in 1967 to help manage any fallout from a second federal lawsuit that forced the comprehensive desegregation that Wilson had averted a decade earlier.

Reed spent just two years at Wilson — but what years they were. The black student population increased tenfold to more than 300. Vietnam, drugs, the King assassination. "Vince was navigating all of that, everything," said Jack Koczela, Class of 1970. Reed ran the school with equanimity, formidability and decency. He studied the yearbook to learn students’ names. Reed went on to an acclaimed, five-year run as superintendent and ended his career as an executive at The Washington Post. Post columnists Colbert I. King and Courtland Milloy and former Post publisher Don Graham have backed Reed's name for the school. "He is a hero with a capital H," Graham told me.

But last month, I listened in as the editors of the Wilson student newspaper, the Beacon, deliberated over Zoom which name to endorse. (I'm an informal adviser to the paper.) One student mentioned Barry's criminal record. No one liked the idea of August Wilson. The editors rejected Northwest, the overwhelmingly white city quadrant where the school is located because it reflects "gentrification and racism", one said, and the student body comes from across DC. They liked Jackson and Reed because of their personal connections to the school, but Jackson, the editors decided, offered more.

As a black woman who integrated the school, the students wrote in an editorial, Jackson is the antithesis of Woodrow Wilson, a white man who segregated the Government. They pointed out that, no small thing, Jackson would be the first woman on the marquee of a DC high school. And, they wrote, she would represent something beyond her race or gender: a message that "teachers matter just as much, if not more, than any president or famous figure".

Reading that, and contemplating the story of Jackson's life and what she endured and accomplished, I went back online and changed my vote. (Of the more than 6,000 responses, Reed and Jackson split the Wilson educator support, combining for 36 per cent. August Wilson drew 29 per cent and Northwest 15 per cent, with the remaining candidates in single digits.) "It's not that Edna was first — that's important — it's that Edna was an instrument of change, both for white students and for the few black students who had to negotiate their way through that place," said Houchins, the Bates professor. "That's reason enough."

At the end of 1958, Jackson posed before a classroom of white students for a photographer from the Post. She wore a smart jacket and pearls, her signature cat-eye glasses and a gentle smile. "Mrs Edna B. Jackson, Negro history teacher, is a favourite of Wilson High School students," the caption read. In the accompanying article, schools superintendent Carl F. Hansen pronounced the desegregation of DC’s schools "complete as of today" and "a miracle of social adjustment". Jackson wasn't quoted. Not a single black student graduated from Wilson that academic year.

The name above the entrance to this school or any building can only do so much. The composition of Wilson’s AP classes, clubs, lunch tables and sports teams reflects enduring educational shortcomings and racial divides. The discovery of swastikas in school bathrooms last year and a report in the principal's weekly newsletter this autumn that students used racial slurs while Zoom-bombing classes reveal deeper societal problems.

But if we're going to name buildings after people, we should recognise people whose legacies are tangible, whose biographies are more relatable than a Wikipedia entry. I can see teachers using Jackson's life and the ghosts in the building to explore the history of desegregation. And I can hear the student section at basketball games chanting, "Ed-nuh! Ed-nuh! Ed-nuh!"

• Stefan Fatsis is the author of Word Freak and A Few Seconds of Panic, and a cohost of Slate's sports podcast, Hang Up and Listen. His daughter graduated from Woodrow Wilson High School in June