Ganesh's earliest name was Ekadanta (One Tusked), referring to his single whole tusk. There are a few variations on how Ganesh broke the other tusk. One variant states he lost it in a battle when struck by Parashurama’s axe. Ganesh allowed himself to be hit out of respect for Shiva, who gave Parashurama the axe. Shiva also decapitated Ganesh, giving him an elephant head in the first place…
I always found this Hindu Deity interesting an illustrated him in this graphic style.