The beginner student probably thinks the ending is ου.

Those that are told the stem ends in ο might be tempted to conclude the actual ending is υ. At least one popular introductory text teaches this but it’s incorrect.

Those more familiar with the sandhi rules might conclude the ου could come from ο+σο or ε+σο via οο. Those who know some Homer might speculate an ο+ιο, but ου is also found in Homer (especially in the pronouns) which might seem confusing.

Those who study proto-Indo-European might know of *osyo becoming *ohyo in Proto-Greek then *oyyo.

How should this be modeled synchronically? I think there’s too much of a tendency in morphophonology to adopt an “ontogeny recapitulates phylogeny” approach and assume that speakers are storing a historical underlying form and then replaying millennia of sound changes.

The problem here is there’s no way a Koine speaker would have reconstructed *osyo during acquisition. In my stem+ending annotations I tentatively used ο+ιο but I’m reconsidering that. There is no evidence I can think of that would have helped a native Koine speaker choose between ο+ιο, ο+σο or ο+ο as underlying.

And given that there are a class of 1st declension masculine nouns whose genitive singular ends in ου despite the α stem ending (which could not result in ου unless the α was actually dropped), it may actually be best to view the speakers’ knowledge as the ending just being “ου”— the naïve view we wrote off at the start.

At the very least, we need to be very careful when saying “the stem is X, the ending is Y” as to whether we are trying to explain the form historically or the speakers’ synchronic knowledge.