There are far too many gods and epithets to name them all, but I'll try to help you out by naming a few. Some of them don't necessarily have to be uppercased when you come across them in text, but anyway heres some just off the top of my head:
Zeus: cloud gatherer, lord of the lightning bolt, loud thundering, son of Kronos, Aegis bearing
Athena: Pallas, wide-eyed, white-armed
Apollo: far-shooting, Delphinius, Pythian, archer god, god of the silver bow, Phoebus, Lycian
Poseidon: earth shaker (basically eanything having to do with shaking/moving land)
earth hugging okeanos, bain of men (ares) lover of smiles (aphrodite) owl eyed hera, crooked minded kronos, crafty kronos, mother tethys, bandy legged hephaistos....
theres so many more but i cant remember all of them. a lot of common epithets have to do with where the god came from. Where they were born or a place they have a connection to through another myth.
In mythological since yes
Greek gods/goddesses did not have "last names" they had titles/epithets.
The Trojan War gave the classical Greeks it's heroic ideal and several mythological gods.
Mercury was a Roman god.
Olympians
Hermes is a mythological god. Gods don't have childhoods.
Greek myths are about the Greeks and contain Greek Gods and mythological characters, whilst Roman myths are about Romans and contain Roman Gods and mythological characters.Hope this helps! :)
The most often used mythological symbol for lust is the satyr. And any of the "trickster" gods will do for Lie - try Coyote
Greek Gods are mythological beings. They don't exist. But, they were located in Greece. America as a country did not exist during the time of the Greek Gods.
Many gods fatherd several other gods and heroes. But I think the answer you're looking for is Zeus.
Pantheon means; (pan) "all" and (theon) "gods".
Mount Olympus is a mythological place. It's not real.