The child was born on May 23, the day Prime Minister Narendra Modi's BJP returned to power with an overwhelming majority.
The infant's mother, Mehnaaz Begum, wanted to name her son after the Prime Minister and stood her ground in face of expected opposition from her family.
The newborn's father Mushtaq Ahmad, however, supported his wife and the baby was named after Modi.
The baby's grandfather Idris said that the family agreed to the name because of their admiration for the Prime Minister.
Commenting on the development, BJP spokesman Harish Srivastava said: "There could not be a bigger example of the 'Sabka Saath Sabka Vikas' concept that did not differentiate between Hindus and Muslims. It is only the pseudo-secular forces that want to create an atmosphere of terror. Muslims are beginning to realize that the Modi government means well for them too. This family has proved it."
The news comes a day after the All India Muslim Personal law Board issued a statement asking Muslims not to "worry" over the BJP's victory. "We have faced several critical situations and this time too we will tide over it," it said in a statement.
AIMIM MP Asaduddin Owaisi, while addressing the media on Thursday as the Lok Sabha results came out, said tough times may await the nation's marginalized communities in days to come. He also said that Modi has busted the myth of Muslim vote bank and instead proved that a "Hindu vote bank" exists.
( With inputs from IANS )