Legendary Weapons

Not much is known about legendary items as of now, but Light said that "Legendary items will be crafted and will be made of a few difficult-to-obtain materials, such as ones from completing difficult quests".

First legendary
It is known that this is the first legendary item.

Although it's also unknown if first is referring to first made or first to become accessible in game.

This sword is as of now unnamed.

Unknown sword
This is the first sword that light has announced to be legendary although not the first legendary made.

This sword is currently unnamed.

Trivia

 * 1) The 1st Legendary weapon was been announced on the 10th of April 2018 on Light Games' twitter.
 * 2) The 2nd Legendary Weapon was announced on the 18th of February 2018 on Light Games' twitter.