Athens was named after Athena, the goddess of wisdom and courage.
Zeus decided that each of the rival gods, Poseidon and Athena, would make a gift to the city who would then decide which god would be their patron. Poseidon struck a rock with his trident and caused a spring of water to come out from the ground, assuring the citizens that they wouldn’t face any time of drought. However, the people were not exactly enchanted with his gift because the water from the spring tasted salty, like the sea over which Poseidon ruled. Athena planted a seed in the ground, which grew up to become an olive tree. The citizens liked this gift better because it would give them food, oil and firewood. They acclaimed Athena as the patroness of the city.
This myth has a point of reality: many olive trees are found till today in the suburbs of Athens, but the city indeed faces problems of drought, especially in the summer.