In every appearance of Shredder, he very obviously wears his helmet, although it only makes a few significant appearances in which it is brought attention to. This helmet is never given any special name until Teenage Mutant Ninja Turtles: Mutant Madness, in which it is called Kuro Kabuto, as it was in the 2012 TV series.
Teenage Mutant Ninja Turtles (arcade game)[]
Shredder's helmet can be knocked off from both himself and his illusions as their health nears its nadir. This can be useful in telling whether the player is currently attacking Shredder or the illusion, as the illusions have lower health points, and thus, their helmet will come off much quicker.
Teenage Mutant Ninja Turtles: Mutant Madness[]
The helmet acts as Shredder's upgrade equipment, and receives its name for the first time, Kuro Kabuto.