In about 1774, the Potawatomi founded two villages in the area of what is now Ann Arbor
On February 14, 1824, John Allen and Elisha Rumsey staked their claim to what they called “Annarbour” and registered a plat of land west of Detroit on May 25, 1824, the earliest known use of the town’s name. They arranged for their village to become the county seat of Washtenaw County.
Allen and Rumsey decided to name it for their wives, both named Ann, and for the stands of Bur Oak in the 640 acres (260 ha) of land they purchased for $800 from the federal government at $1.25 per acre. The local Ojibwa named the settlement kaw-goosh-kaw-nick, after the sound of Allen’s sawmill
Sources:
Ann Arbor, Michigan Wikipedia entry
For other versions of the story, see The Making of Ann Arbor, Chapter 1