Changing one's name after marriage is very personal decision. Some might be ok to change name and others might not find it necessary. I choose to change my name after marriage and adopt the surname of my new family. I don't believe your last name is what defines you. Yes it is part of your identity and so is all your relations. When you build new relationships your identity is also changing or at least these relations are also adding on to your identity.
For Anokhi also the choice should be hers but I am confused why all of a sudden she is having issue with this. After maang main sindoor wali marriage she was quite happy to be called Mrs Anokhi Shaurya Saberwal. So why is she having issue now? Am I missing something?