passport renewal and name issue

[sashakrishna]

My passport is going to expire by January 2021. I am on h1b and I got a new job .While filling the documents I realized my passport is going to expire. When I contacted the new employer they asked me to apply for renewal. My issue is my old passport dont have firstname and given name is Sasha Krishna. So in visa its FNU Sasha Krishna. But new VFS application wont allow for blank first name. If I fill FNU as first name will it consider as a name change? If I split my name as Sasha as first name and krishna as last name, i think i need to go to Social security office and all other places like dmv to change my name. In this situation I am not sure how safe to go to all these crowded places.
Is there anyone went through similar situation? if yes what you did when you renew your passport? Also what if my new employer filed my h1b with old passport?

[Walia_nidhi]

I have a similar kind of issue. My surname is blank in Indian passport and I have to add surname (both my father and mother name has surname in my passport). If anyone can help what process I should follow?
I have checked the change in name protocol but I am still unsure if court notarized document would be sufficient or I need 2 newspaper advertisement as well?
Any help would be appreciated!