Name change before H1B stamping

[shipahwa]

Hi All

My name in passport is only first name. Surname column is blank. My H1B petition is approved with the name FNU Shivani.
I also have a B2 visa with the same name.

Before stamping i want to modify my name in the passport and add my surname to it.
1) Would this also affect my H1B petition as the passport number and Name would be changed.
2) Do i have to file for a amendment and if so how long does it take.

All the help would be appreciated.
Thanks in advance
Shivani