King Street was named by David Maynard in his 1853 Plat of the Town of Seattle, one of the first three plats laying out the street grid. (The other two plats, north of Maynard’s, were filed by Carson Boren and Arthur Denny). Maynard, a staunch Democrat, named many of the streets in his plat for Democratic leaders, including Andrew Jackson, John B. Weller (Governor of California), and Joseph Lane (Oregon Territory’s Congressional delegate).
King Street is named for William Rufus DeVane King, who was elected as Franklin Pierce’s vice president in March of 1853 and died six weeks later. He remains the shortest-serving U.S. Vice President. King died about a month before Maynard filed his plat. King County was also named for William King, and Pierce County, our neighbor to the south, was named for the President.
King County has since been re-namesaked in honor of Martin Luther King, Jr., but presumably the street is still named after William Rufus.