According to the oldest story by Titus Livius: During the war between Romulus and Titus Tatius, begun after the rape of the Sabine Women, the Roman commander Hostus Hostilius (grandfather of King Tullus Hostilius) was killed in a duel by the Sabine commander Mettius Curtius. Romulus came with many soldiers to take vengeance upon him; Mettius Curtius had no way out, and fell with his horse into a marsh. Romulus thought he was dead, so retired to his headquarters on the Capitoline hill's Arx. But the Sabini went there, found their commander still alive in the marsh, and rescued him. The place henceforth took its name from Mettius Curtius.
A second story is told by Marcus Terentius Varro: in 445 B.C. lightning hit a spot in the Roman Forum; In accordance with the Roman religion, the place was declared sacred and closed with a palisade by the Consul Gaius Curtius Philon. The place took its name from that Consul's nomen.
A third story, again from Titus Livius, tells that in 362 B.C. a chasm opened up in the middle of the Roman Forum. The people began to try to fill it, putting in several kinds of votive offerings, but the abyss remained. So they asked the Auguri what they should do: they answered that the chasm would be closed only putting inside it "the most precious thing of all". The Romans tried to guess what that could be, and tried many different offerings, but the chasm still did not close. Then a young Roman eques named Marcus Curtius had an inspiration: the most precious thing of Rome had to be the courage and strength of Roman soldiers, the real power of Rome. So he wore all his weapons, and riding his horse threw himself as a sacrifice into the hole, which was immediately filled. The heroic act was honoured by the Roman people who gave to the place the same nomen of the young and brave horseman.
In 1553 CE near the Column of Phocas was found a bas-relief showing the horseman Marcus Curtius falling down the chasm. A copy of the original bas-relief (visible in the nearby Capitoline Museums) is standing by the side of the Lacus Curtius, in the middle part of the Roman Forum.