Does name change in passport not good enough to change the name in I-94 ?

USA H1B Visa
1 
Hi,

I was facing an issue that passport had my first name as FNU and my last name had both my actual first name and the surname .

I got it corrected in my passport recently .So my new passport has a proper first name and last name . So my next step was to get my I-94 corrected . But when i went to the USCIS office in chicago , they refused to change the name in my I-94

They say that I-94 name is based on my visa and not my passport . I am on H4 visa right now and i am planning to apply for H1B visa . Will my I-94 with first name as FNU cause any issue in filling a H1 visa ?. Can i use my new passport name in all my documents while filing a H1B.

Did any one else phase the same problem ? . Please let me know if any one has any suggestions to me
2

It must not be any problem…

3

I think you should use the name as per your new passport going forward. Once your petition is approved, that will come with a new I-94 and the name should be updated on it.