As I fill in her name on these forms, how do I write it, first name patronymic last name?
Or just first name and surname?

Either I think would be OK... I put it exactly as it was on her passport...

I let my fiance fill out her own part of the forms just as the questions were asked.

Bruc

I did first name as first name, family name as last name, patronymic as middle name. No problems.

Ensure that you stay consistent throughout all your sheets. If you're going to label her G-325A one way, do it that way on her I-129F as well.

If she does not mind (however, she might) just first and last names are OK. And consistency: it must go like this through all other documents. And it will continue in Driver's License, SS card, etc. People were making mistakes, and my credit applications were rejected a couple of times just because people in US are not used to see middle names in DL's, etc. and would take my middle name (my dad's first name) as if it was my last name. Sure it did not match with SS#.

IF the international passport has the three names and I fill out all docs with just her first and last, it should not be a problem?

No. It should not be a problem.

She has a first name, she has a last name, but most importantly, she has a first name and last name with a birthday and national ID number that nobody else has.

That's all they really need, to confirm that she is who she says she is, and that she's the one you've made the application for.

Well the new International Passport has arrived and I notice it only has her first name and last name, I guess I will just use that on her documents even though her birth and divorce translations of course have all three names.