Eris was officially named by the International Astronomical Union on Wednesday. It had previously been known as 2003 UB313.
Astronomers were divided over how to classify the object because there is no universal definition of what constitutes a planet.
Some people argued that Eris was the tenth planet in the solar system as it was larger than Pluto, but others said Pluto itself could not be considered a planet.
Astronomers last month voted to shrink the solar system to just eight planets and downgrade Pluto to a "dwarf planet".
That category also now includes Eris and the asteroid Ceres.
After Pluto lost its planetary status, hundreds of scientists circulated a petition protesting against the decision.
After the furore caused by the change, Michael Brown of the California Institute of Technology, who discovered Eris, said the name was an obvious choice, saying it was "too perfect to resist".
Brown had nicknamed it Xena, after the main character in the TV show Xena: Warrior Princess, until the official designation.
In mythology, Eris caused a quarrel among goddesses that led to the Trojan War.
Eris' moon has also received a formal name, Dysnomia, the daughter of Eris known as the spirit of lawlessness.
Eris, which measures about 115km wider than Pluto, is the farthest known object in the solar system at 14.5 billion km from the sun.
It is also the third brightest object in the Kuiper belt, a disc of icy debris beyond the orbit of Neptune.