http://www.sacred-texts.com/hin/db/bk06ch15.htm...As this son was born due to the burning of the Aranis, the boy was named Mithi, and as it came out of the body of Janaka, the boy was named Janaka. O King! As the King Nimi lost his body, i.e., became Videha through the curse of Vas’istha, all his descendants were known as Videha.Thus the son of Nimi was well known as the King Janaka. He built a beautiful city on the banks of the Ganges; the city became famous also by his name (Janakapuri). ... All the Kings of this line became famous by the name of Janaka and all were endowed with the Supreme knowledge and known as Videha. O King! I have now described to you the story of the King Nimi who got disembodiedness (Videhatva) out of the curse.
Hence names 'mithlA', 'janaka' and 'vidEha'.