If you google it you'll get nothing or Meaning unknown, PERHAPS derived from Greek αθηρ (ather) "sharp" and αινη (aine) "praise" which is for sure very wrong. In original form it is Αθηνα (ATINA), In a Macedonian language or like Greeks like to say Slavo-Macedonian Atina is derived from ATA-ATINA-old church Slavonic or Slavo Macedonian-TATINA-modern Macedonian meaning father's girl. And how the goddess Athena was born: After he swallowed her pregnant mother, Metis, Athena is "born" from Zeus' forehead as he grasps the clothing of Eileithyia on the right; black-figured amphora, 550–525 BC, Louvre. So you see why she is the FATHER'S GIRL- SHE WAS BORN BY HER FATHER. Because there is no material proof that Slavs came into Macedonia, actually Slavs are just a theory who was accepted without any material or archeological proves for any kind of so- called Slav tribes appears that those tribes who were called Slavs are actually indigenous people of the south Balkan. If we consider that the Athena is founded by indigenous Pelasgians and not by Hellens who were newcomers than you have the answer who gave the name ATINA.
My first daughter's name is Athina, the original form of Athene. She is the goddess of wisdom in Greek mythology and associated with the Owl. Athina is the goddess of Athens, she gave the city the olive tree as a present, that was one of the most important crop of ancient and even today's Greece. My daughter has 100 olive trees on our field and at the age of 2 she is already looking after them. :)