Probably a variant spelling of Tullahoma, a town in central Tennessee, 55 miles northwest of Chattanooga.
Tallahoma—a. wooden-hulled, sidewheel, "double-ended" gunboat of the Sossacus-class—was constructed at the New York Navy Yard and launched on 28 November 1862. However, since her construction was not completed until 1867—when the Civil War which had prompted her construction had ended—the ship saw no service. After a brief period in ordinary at New York, the ship was sold on 29 August 1868.
Documented as Mary M. Roberts on 10 November 1868, the erstwhile gunboat was converted to a barge on 21 December 1870, and she disappeared from the lists of merchant vessels.