FNU in H1B visa

I don’t have Last Name/2nd Name on my Academic documents and passport.

From my understanding this will give me hard time i getting my SSN and Driving License in US, If thats the case then after the stamping done, getting a new passport with both names corrected and re-stamping shall solve this issue ??

Or do I need it to be rectified in all the academic documents as well ?

Listen - hard time is an understatement. you will face big-time hard-time with this. I suggest you right away get a fresh passport with a last name. all you would need is a name change affidavit and the process around that. no need to get acad certificates corrected.

with the new passport in hand, then appear for stamping.