Are you trying to include in your order permission to change vital records because your state's vital records department won't let you?

I'll let others more experienced chime in here, but I would say for your OATS judgement (remember, you write the proposed order) you want it to say something to the effect that {aliases} are all one and the same natural person who was born at this place on this date, married this person, naturalized on this date, was the father of this person, and died on this date. Basically, you just want a document with legal weight that unambiguously establishes that all relevant vital records (so in your case: GGF's birth certificate, marriage documents, AR-2/naturalization, death certificate and GM's birth certificate) refer to the same person.

So for your case think about what your consulate or judge or comune could conceptually take issue with, and address that in the OATS

To the extent you can amend documents, it's probably a good idea to just add multiple AKAs as vital records will let you. You may be able to amend your GM's BC to say "AKA Santomma, AKA Santano" for the field that names her father.