Ekadanta means one with one tooth. Ganesha has one broken tusk. One story is as such that when Ganesha was writing the Mahabharata, his pen broke. As a result, he himself broke his tooth and wrote the Mahabharata with it to finish what he started. Another story is that when Bhagwan Parshuram was visiting Kailash to meet his Lord, Shiva. But, he was stopped by the bodyguard, Ganesha. A fierce battle broke out between Parshuram and Ganesha. They used many different weapons and astras. But at last, Parshuram used his axe against Ganesha. Ganesha realised that the axe was given to Parshuram by his father. So, Ganesha did not resist it and let him strike it. As a result, Ganesha’s tooth broke and was named Ekadanta.
Another story is that when Ganesha was fighting Gajamukhasur, in the battle, his tooth got broken. Later, Ganesha defeated him with that tooth and made him his vehicle (Mooshak).