Name change issue

Hi All, My name is Aarti Baloni. After marriage, I got my name changed to Aarti Baloni Ajbani. Now the problem came when the MCG (Municipal Corporation of Gurgaon) issued a birth certificate for my baby in 2018 and mentioned by name as " Aarti Ajbani" in the certificate. 1) Is "Aarti Baloni Ajbani" and "Aarti Ajbani" same? Do I need to have my name updated in the birth certificate? PLEASE NOTE THAT I DO NOT HAVE ANY DOCUMENT THAT MENTIONS "Ajbani" anywhere. All my ID proofs are by the name "Aarti Baloni" only. 2) I am a little unsure of what documents require to be changed. Can someone please confirm me. 3) Also, all my ID proofs have a mention of my parent's residence which apparently stands incorrect now since they have also moved from that place. I anyway have to change the address in my adhaar/passport to reflect that. 4) My husband works in IT and can get an opportunity to fly to the USA. That means I am eligible as a dependent and can fly too. This name difference in my docs and marriage certificate will cause an issue? Thanks in advance