I would say Eldarion is Quenya and might contain a patronymic.
Instead of Eldar-ion with a plural 'Elves' I think (not sure) it's possible we might have Elda-ri(g)-on with *rig- 'crown' plus a masculine, as similarly, perhaps, in Telperion, or more certainly the element 'crown' in Sindarin Galadriel 'Maiden crowned with gleaming hair'
On the other matter, good question. I can say without much delving (being lazy) that at the time Etymologies was being constructed go- was said to be used for patronymics in Ilkorin (go-Thingol).
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