Hi Mler,
thank you for your reply.
GF's birth certificate from Italy states his name as Odoardo (Edward). That's what I assume the NYC Consulate will want to see in his all further vital recods.
GF appears as Charles in Naturalization certificate, which can't be amended as far as I know.
So I guess ...

Dear All,
I'm new to the whole process of obtaining Italian citizenship via jure sanguinis.
We are doing this through my spouse's grand father.
There are some name and date discrepancies in the documents.
For example, he was born as Odoardo. Came to USA as Eduardo (ship manifest). He got married as ...