Justice Indermeet Kaur issued notice to the Centre and the Central Board of Secondary Education asking them to reply by September 7, the next date of hearing.
The court was hearing a complaint filed by a north Delhi resident Hema Bawari, who later changed her name to Himanshi Bawari but was not able to effectuate it in the CBSE records.
Advocate Satya Ranjan Swain, counsel for Bawari, told the court that amendment to the Rule 69.1(i) of the Examination Bye-Laws are unjust, unfair and unreasonable.
"It is humbly submitted that the earlier law prior to the amendment - which provided 10 years time limit to make necessary changes, was relatively more reasonable than the existing one," the plea said.
"It is unreasonable that the name of the petitioner cannot be changed only because she failed to change it before the publication of her results," the petition said.
In her petition, Bawari claimed that she passed her Indian School Certificate Examinations in March 2009 and she changed her name the next year from Hema Bawari to Himanshi Bawari due to astrological reasons.
The name change was published in a newspaper and also in the Gazette of India.
The petition also said that her Aadhaar Card, PAN Card and the Election Identity Card were made with her new name Himanshi Bawari.
She approached the CBSE for changing her name in the certificates as she intended to pursue higher studies abroad, the petition said.
The CBSE, in a letter sent to her on July 7 this year, said that subsequent to the amendment in Rules 69.1 of the Examination Bye-Laws, the change in a candidate's name may be considered only if the desired changes have been specifically admitted by the court of law and notified in the government Gazette before the declaration/publication of the concerned examination result of the candidate by the Board.
"The amendment is contrary to the Right to equality as enshrined under Article 14 of our Constitution - which is a bulwark against any arbitrary or discriminatory state action," the plea claimed.