name difference on H1B approval notice vs new passport

Hi

My Name is XXX YYY ZZZ where ZZZ is my last name
on passport it is mentioned as
GIVEN NAME XXX YYY ZZZ
SURNAME BLANK

I have applied for H1B and my petition got picked up in lottery, I got the approval notice where my name is mentioned as “XXX YYY ZZZ, FNU”
I researched at google and find I will be in trouble if I enter in USA with surname as FNU which will impact on SSN and driving license etc.
so I want to amend my name on passport after splitting my name but worried about the name consistency on H1B approval notice(I797b) vs name on my new passport.
will it create issue if I amend my name now before getting the stamp.
could you help me to figure out the best way to do it.

Thanks in advance