She was known for not sleeping with gods at all, just with mortal people. The Romans celebrated her worship from March 19-23. During this celebration, all teachers in the Roman empire were paid their year's salary, linking the goddess Minerva to our teacher Minerva here.
Where the goddess Minerva is responsible for crafts and arts, our teacher Minerva is in charge of transfiguration. Both create items, the goddess through working by hand, the teacher through working with magic. In the end, results are the same. Items like wood or animals are turned into other items.
As the goddess of wisdom, her symbol is the Owl. The owl, as we already know, is a magical creature in the Potterverse. Our Minerva allows Harry to skip class to get his own owl treated because it was wounded. She doesn't allow anybody to break any rules, but she does allow Harry to skip a class because his owl was wounded (OotP). The latin word for owl is Strix and multiple owls are Striges, which later became the Italian word Strega. (Strega means witch by the way.)
The goddess Minerva is a virgin goddess. We don't know yet if our McGonagall is still single, but I wouldn't be surprised if we find out she is.
As goddess of (protective) war she is the counterpart of Mars, the god of (offensive) war. She is often displayed in full armor with a spear. She aided Perseus in killing the Gorgon, and she therefore has the image of the Gorgon's head on her shield. (A Gorgon is a woman with snakes for hair.) Lovely how the real Minerva likes killing snakes. In images, the goddess...