The first name of the town was Tauromenium, which is up to now preserved even if transformed in Taormina, and it means built up area in Tauro, the mountain upon which it rose. According to the historian Diodoro, Siculians and Greeks too gave that name to the town. 
But there are a lot of legends around the origin of the name. One of these tales is about a Minotauro, which is represented in ancient coins, and by which the name could derive.
Another evokes two princes from Palestina, Taurus and Menia, who would have founded the town, giving it the Tauromena name. 
Around Taormina there are other many legends. Some of them have Pitagora as protagonist, who would have spoken in the same day to Taormina and to Metaponto, would have made Taormina adopt the laws of Caronda, would have placated the erotic furies of a young taorminese playing his magic flute. In reality, Pitagora lived a historical period in which Tauromenium was not still founded.