It was named after ancient Roman philosopher, mathematician and astrologer Lucius Tarutius Firmanus.

The surface about Taruntius has an unusual number of ghost craters and lava-flooded features, especially to the southwest in the Mare Fecunditatis.

The outer rim of Taruntius is shallow, but forms a veined, complex rampart in the nearby mare, especially to the north and southwest.

One patch is located just south of the central peak and the other falls on the sides of the northern rim near Cameron.

[4]: 333 By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Taruntius.