First name Last name mismatch in school certificates and passport

[Haritha23]

I need to apply green card for my father. He does not have a birth certificate but I believe we can submit his school certificates in place since he was born before 1970.

The issue is that there is a mismatch between his first and last name in all his certificates and his passport.

For example assume his name is Venkata Krishnan Raghavan. All his certificates mention his name in the following format:

Last name as 'Raghavan' and first name as ' Venkata Krishnan'

But  in his passport they made a mistake and mentioned Last name as 'Raghavan Venkata' and first name as 'Krishnan'.

He has travelled to US multiple times with this passport. Would it create an issue with the green card processing with this name mismatch? Can we submit some other document along with the application which can correct this issue/ establish that both names are of the same person or will he have to get his name corrected in the passport before applying for the GC?

Thanks in advance for your help.

Haritha