The Bachchan family welcomed the baby girl Nov 16. Since then Bachchan junior has asked fans to suggest names for the new member on a micro-blogging site.
"The suggestions still pour in and still we haven’t managed to finalise a name. Evenings are spent reading out all your suggestions in front," Abhishek posted on his Twitter account.
"Of the family and trying to decide. Will decide soon. Many thanks again. Lots of love," he further tweeted.
Meanwhile, Amitabh Bachchan is busy hosting well wishers.
"A host of visitors for the baby and the joy and blessings they leave behind … thank you. The name suggestions keep coming in," he tweeted.