So the Riordan theory in his books is that when the population of the earth expanded, those that worshipped them changed their names and the reason of worship. This is why the Romans seem much more militaristic and it's stated that for example if Zeus changed to his Roman form of Jupiter (they're still the same God) his personality changes to become much more militaristic and warlike to base on where he's located.
So if Zeus as Jupiter had a child they would technically be a 'Child of Jupiter' and not Zeus but would Zeus not be willing to protect them still? If we had something like a catastrophe befall the Roman children they would be forced to the only other safe haven. Olympus Academy.
Would throw in a cool RP aspect since the school itself is smaller this year because of the arguing amongst the clouds in Olympus itself. These Roman kids come in and shake it up!
@Kidd Congrats!