Since the first "modern" DC public school was built in 1864, and promptly named for the mayor who built it, the public school and charter school systems have named 255 schools for individual people. Among them are 32 known slave owners, 10 former slaves, 10 abolitionists, 2 people who joined the Confederacy, 17 civil rights leaders, 26 presidents and 32 mayors or other city officials.
Here's how DC schools got their names
Through the first half of the 18th century, there were few school buildings in Washington, DC. Many classes were taught in rented space, churches, temporary frame buildings or firehouses, especially in Washington County, the then-rural areas at the edges of the District. What schools existed for free black students were mostly in church basements, but a couple of privately run schools had their own buildings.
In 1862, schooling became mandatory for all children, with free schooling was now available past the elementary level. To meet the need for space, in 1864 the school board authorized the construction of 30 new school buildings, with more to follow. In fact, schools were added at such a rapid pace, and at such a high cost, that it contributed to bankruptcy and the end of territorial government in 1874.
Most of the early school buildings were named for their location, such as Western School and Eastern School. The first public school named for a person was the Wallach School near Eastern Market, built in 1864 and named for then-mayor Richard Wallach. Throughout the rest of the 19th Century, the school system would add more than 60 school buildings, some hosting multiple schools, and these would be named primarily for US presidents, DC mayors and commissioners, and "Great Men" of national importance.
After the DC Commission (a precursor to today's District Council) lost control of the school boards in 1906, the school board began honoring more teachers, principals, school board members and school administrators. Nonetheless, all but three DC chief executives between mayor Robert Brent (1802-1812) and board president C.H. Rudolph (1910-1913) had a school named for them. So did every president between John Adams and Calvin Coolidge, except for Benjamin Harrison and Warren Harding.
Names weren't always intentional
While some of the school names were chosen to honor people, it seems others did it by accident. Three schools originally named for their location, Greenleaf, Benning, and Garfield, later became known by the name of the famous person for whom that location was named. Only in the case of Benning was I able to determine that this was done officially.
Most interesting is the case of the Adams Buildings. The Old Adams Building was originally named for John Adams. It was always referred to as the "Adams Building" as, school buildings were commonly called by just one name. Despite a tradition of naming schools after presidents, there wasn't one named for John Quincy Adams, because he and Benjamin Harrison were intentionally skipped to avoid confusing them with their older relatives.
However, at some point in the early 20th century, school documents began referring to the Adams Building as the J.Q. Adams Building, most likely due to the very confusion they had tried to avoid. When the city built a new school to replace it, they called it the John Quincy Adams School (from which the Adams Morgan neighborhood gets part of its name) and carved his name in the marble tablet above the main doors. Thus, it appears that poor record keeping led to the "John Adams School" being renamed the "John Quincy Adams School" without anyone deciding to do so.
Some schools were renamed due to controversy
A few schools in DC have had their names changed, dropping one person for another, but not to revoke the honor of the original namesake. Rather, schools are renamed to make room for someone new or, in the case of the L'Enfant School, to avoid a name that might otherwise be embarrassing (parents feared it would be known as "The Infant School"). However, a national movement is underway to remove the name of Confederate heroes from schools, and in at least one case in DC there was an effort to replace a school's namesake because he'd been a slave owner.
There have only been two schools in DC named for people who served in the Confederacy, and only one is still in use. Both are in Capitol Hill. John Tyler Elementary is named for the former president who in his last years led the secession movement in Virginia, signed the Orders of Secession, negotiated that state's entry into the Confederacy, and served in the Provisional Confederate Congress. The old Lenox School, now a condominium, was named for former mayor Walter Lenox, who went to Richmond during the war, where he worked in the office dealing with prisoner of war exchanges.
There are currently twelve schools named for known slave owners, and two named for former slaves. However, it is further complicated by the fact that some slave owners went on to become abolitionists or, in the case of Lafayette, always were.
School honorees are mostly white, mostly male
As for what kinds of people get honored with a school named for them, about 80% are men and 67% are white. Teachers, principals, school administrators and school board members combine to make up about 40% of those for whom schools have been named for, about the same percentage as all political leaders.
A full list of the named schools, a brief description of who they were named for and why they were honored can be found here.