The 34-year-old actor and Soha, 38, welcomed their first child on September 29.
Kemmu took to Twitter today to reveal the name of their daughter.
"We have named our daughter Inaaya Naumi Kemmu. Little Inaaya is happy and healthy and she thanks all of you for your love and blessings," wrote the actor.
He had announced the arrival of his little one, who was born on the ninth day of Navatri festival, on the microblogging site.
"We are over the moon to share we have been blessed with a beautiful baby girl on this auspicious day. Thank you for the love and blessings," he had written.
Soha announced her pregnancy in April 2017.
On the work front, Soha was last seen in the film "31st October". Kunal will be seen next in "Golmaal Again" scheduled to release on Diwali.