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No, the Greek goddess Athena did not love Heracles; she was goddess of heroic endeavor so Heracles would ask her help and favor.
No, the temple and city/towns were named after the Greek goddess Athena. They were named after her in remembrance to her, for favor/patronage, or for worship.
Athena was the Greek goddess of wise counsel, the defence of towns, and heroic endeavor, her advice and favor made heroes possible - without her there would be no heroes.
No, in classical mythology Athena was a maiden (like Artemis and Hestia). However she did favor many people.
Athena is the goddess who protects and assists Odysseus in Homer's epic poem "The Odyssey." She guides and supports him throughout his journey, often intervening on his behalf with the other gods. Athena's favor is a key factor in Odysseus's eventual success in returning home to Ithaca.
Demeter is the goddess of harvest or agriculture. Some sources states that she is also a goddess the favor the sacred law of marriage and order as well as the goddess of life and death.
Victory in all games and war was under her favor.
Well, Aphrodite is the Goddess of beauty so I would say her although I do Favor in Selene
Odysseus
You'd be labeled pagan, but certainly if you pleased Artemis you'd believe to have her favor.
Being the goddess of wisdom she probably brought knowledge to the people she had in favor. She was also a very kind goddess unlike the rest of the gods. In one myth, a man saw Athena bathing and was blinded, she then gave him a pack of snakes who would protect him plus gave him the sight of prophecy.
Τυχη, whose name is normally transliterated as "Tyche" (following Latin convention), but would be more faithful to Greek if transliterated as "Tukhe".