Why did Athena the Greek goddess give her name to Athens?

Athena and Poseidon both wanted to be the patron of Athens so they had a competition. Poseidon gave the city a river. At first, the people liked this . Then they realized that it was salt water and they couldn't drink it. Athena gave them an olive tree which was much more useful. They could eat the olives, make olive oil and use the wood for fire (which they could use to cook with and to keep warm). Therefore, Athena won and Athens was named after her. Athena and Poseidon have hated each other ever since the war of 1812