The name Athena is one of the well-known titles that the ancient Greeks gave to their so-called gods; she was the goddess of wisdom and strength, the goddess of war and the protector or patron of the city. This is something which is well-known in Greek history, and you can see it in this link:

http://en.wikipedia.org/wiki/Athena

Based on that, it is not permissible for Muslims to use this name, whether it is the real name of a person or the name of a Muslim city and so on, or it is a screen name or nickname, because it seems to be spreading the symbols of disbelief or approving of these names and a type of imitating the disbelievers in a bad way, which is something that is not befitting to the Muslim who affirms the oneness of Allaah, and who raises the banner of faith and Tawheed of the Lord of the Worlds. 

With regard to calling the capital of the Greek state by this name (Athens), that is the affair of the people of that land, and there is no sin worse than kufr. But what we would like to point out to the Muslims is that there is nothing wrong with using this name when speaking of their capital city, but that is by way of narrating or telling about something, when you mention this name as the people of the city want, exactly as the Holy Qur’aan mentioned the names of the goddesses of the mushrik Arabs, al-Laat, Manaat and so on. All of that is by way of narrating and not approving. 

And Allaah knows best.