According to the TOI, South Korean television obtained a leaked internal document from the state that included an "administrative order" to army, police and government officials to establish the new legislation.
"All party organs and public security authorities should make a list of residents named Kim Jong-Un... and train them to voluntarily change their names," it reportedly reads.
The document also warned that those caught with the name Kim Jong-Un would have their identity cards, school diplomas and official documents briskly adjusted. Birth certificates baring the dictator's name would also be rejected.
"Authorities should make sure that there is no one making unnecessary complaints or spreading gossip... regarding this project," the Mail further quotes the document as reading.
The document was first obtained by Park Jin-Hee, a North Korean defector working for the KBS, who left the state in 2008.
"There is no one in the North named Kim Il-Sung and Kim Jong-Il, and there is no doubt the same rule applies for Jong-Un," she said.
The report comes amid speculation that Kim Jong-Un has banned his aides and officials from smoking foreign cigarettes because they are unpatriotic.