How to update immigration documents(I-94.)after updating the passport to correct name(FNU issue)


I recently resolved the FNU issue in my passport and got a new passport with the correct name.

Earlier Passport:

First Name(Given Name): Shourya Nath

Last Name:

Current Passport, SSN, Driving Lisence:

First Name(Given Name): Shourya

Last Name: Nath

F-1 Visa, I-94

Last Name: Shourya Nath

First Name: FNU

I went to both USCIS and CBP and tried to get my I94 corrected with my correct first name and last name. But both of the agencies did not correct them. I am planning to travel home in a couple of months. Can someone advice, would this be a problem ? and how can I get it rectified as in get my i94 corrected.