Afanasiy cannot be spelled Afanasyi, not only based on the principle that while Cyrillic has letters that can be read as ya, yu and ye, the alphabet lacks an 'yi' and... and it just looks silly. Pronounced a-fan-a-see or a-fahn-a-see with the lightest 'h' you can manage. It is not very common these days.
I'm surprised that there IS a Russian form of "Athanasius", considering the fact that "Athanasius" is not actually a very common name. I've always been rather intrigued by Russian names ending in "iy". I wish there was a pronunciation key for this. It's interesting, but preferable for a book character rather than a person, I think.