To scribe the Mahabharat Katha Ganeshji removed one of his tusks to carve a quill from it. He then scribed the epic on palm leaves as the sage Ved Vyas recited it. The scribing took three years!

In south India there is a belief that when ploughing first began on earth, it was Lord Ganeshji who first ploughed using one of his tusks.

In the Uttar Ramayan, Brahmand Puran and Padma Puran there is a reference of a battle between Ganeshji and Parshuram. During the duel, the latters axe fractured one of Ganeshjis tusks According to the Brahmand Puran, it was his left tusk.

There are other names related to his body and virtues.
A few commonly known are listed below

Lambodar from the long lambo, tummy udar.

Gajkarna from the large elephant Gaja ears karna.

Kapil from his ruddy complexion.

Vikat heavybodied.

Bhalchandra having a Chandra (moon) on his forehead bhal.

Dwaimatur one who has dwi two, mata mother Parvati who gave birth to him and Malini a demoness who nurtured him.

Vakratund one who breaks the ego of he who behaves antisocially (Vakra).

Vigneshwar One who removes mayic obstacles vignas.