Anyone who sees this logo will automatically associate it with Versace. I guess that's how popular it already is. I don't really know why it has to be Medusa's head, so I decided to do a little research and here's what I found:First, a little bit of history. I think everyone, at one point or another, studied Greek mythology and encountered Medusa. She's a once-beautiful maiden who was punished for allowing herself to be seduced by Poseidon in Aphrodite's temple. Medusa's hair, her most glorifying attribute, became snakes and anyone who looks at her will turn to stone.
Come the Roman era, Greek myths infused itself with Roman ones. Medusa, in this period, was transformed into a yet again beautiful woman with her snake-hair elegantly donning her head. This facinated Gianni Versace a lot, being a fan of classical art and all.
Him being from Southern Italy also helped in cultivating that fascination with Greek and Roman mythology and decided to use the powerful Medusa to represent his designs, which are for women who were passionate and opulent.