Spouse name change in H1b related situation


I am in below situation and seeking advise.

My wife has not yet officially changed her surname anywhere. I have a son who is 3 months old.
I have got my H1B visa approved and stamped very recently and I will be able to travel to US within couple of months.
I have recently got passport done for my kid in Minor category. The birth certificate for my kid has my wife’s name as - her maiden name + my surname. Due to this my kid’s passport now has my wife’s name as - her maiden name + my surname. But my wife’s passport still has her name as - her maiden name + her maiden surname because she had got it done before marriage. My own passport (already stamped with H1B) has my wife’s name endorsed as - her maiden name + her maiden surname.

Now the question I have is whether I should go ahead and get my wife’s surname changed on her passport to my surname or not. Do I also need to get my wife’s name changed on my own passport? How will it affect my already issued H1B visa stamp?

If I don’t do it, would me and my wife face any problems while travelling to US and during our stay there regarding her surname being different on kid’s passport and kid’s birth certificate compared to her own passport and my passport. Or would the kid face problems in future?

If I do it then what additional documents does are needed to be changed for my wife? Will her degree certificates and other documents be considered valid? Will my wife’s documents be accepted with her maiden name on all her documents but her name + my surname on just her passport?

Appreciate help on above situation.

Thanks in advance!

I am not able to answer your question but I have a small query. I would be very very helpful if you could answer the same.My name in my passport is my maiden name but in my son’s birth certificate the mothers name is my name+ husbands surname.( same as your case) . I was told by the passport helpline that both these mother names should be same for making the child passport. But you were able to get the passport of your child with mother name as in the child’s birth certificate.How was this possible.I will be very grateful if you could guide me in this regard.