From http://www.cr.nps.gov/nr/travel/asheville/pac.htm:
The city as a whole and the square in particular benefited from the generosity of George W. Pack, who offered property for a new courthouse on the condition that the former site become part of the public square, and donated two-thirds of the cost for a monument to Buncombe County native and Civil War governor Zebulon Baird Vance. Local architect Richard Sharp Smith designed the Vance Monument, erected in 1896. The new courthouse (no longer standing) was completed in 1903, and in an expression of civic gratitude, municipal authorities renamed the newly enlarged square in Pack's honor.